rubik (6mar17)

git-svn-id: svn://tug.org/texlive/trunk@43415 c570f23f-e606-0410-a88d-b1316a301751

9 files changed, 5758 insertions, 1822 deletions

diff --git a/Master/texmf-dist/source/latex/rubik/examples.bat b/Master/texmf-dist/source/latex/rubik/examples.bat
deleted file mode 100755
index 1a67e63e77e..00000000000
--- a/Master/texmf-dist/source/latex/rubik/examples.bat
+++ /dev/null
@@ -1,4 +0,0 @@
- latex  --shell-escape  examples.tex
-# latex  --shell-escape  examples.tex
-
-
diff --git a/Master/texmf-dist/source/latex/rubik/rubikcube.dtx b/Master/texmf-dist/source/latex/rubik/rubikcube.dtx
index c2f2411d015..4f57d98a0ee 100644
--- a/Master/texmf-dist/source/latex/rubik/rubikcube.dtx
+++ b/Master/texmf-dist/source/latex/rubik/rubikcube.dtx
@@ -1,10 +1,9 @@
 % \iffalse meta-comment
-%
 %  rubikcube.dtx
 % 
-%  version 3.0    25 September 2015
+%  version v4.0  (03 March 2017)  
 %
-%  Copyright 2015  
+%  Copyright 2017 
 %  RWD Nickalls (dick@nickalls.org) and 
 %  A Syropoulos (asyropoulos@yahoo.com)
 %
@@ -63,7 +62,7 @@
 %
 %
 % 
-% \CheckSum{4105}
+%%% \CheckSum{5683} 
 %
 %%% \CharacterTable
 %%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
@@ -82,7 +81,9 @@
 %%   Right brace   \}     Tilde         \~}
 %
 %
-% \title{The \textsc{rubikcube} package}
+% \title{%
+%       \ifpdf\pdfbookmark[1]{Title}{Title}\else\fi%
+%        The \textsc{rubikcube} package}
 %
 % \author{
 %      RWD Nickalls (dick@nickalls.org) \\
@@ -96,7 +97,7 @@
 %  The \rubikcube\ package provides LaTeX commands and macros 
 %  for  typesetting  Rubik cube (3x3x3) notation,  configurations, and 
 %  rotation sequences  using the  TikZ graphic language. It is part of the 
-%   rubik `bundle'.
+%   Rubik `bundle'.
 %  \end{abstract}
 %
 % \medskip
@@ -104,7 +105,7 @@
 % \begin{minipage}{11cm}
 % \centering
 % \ifpdf
-%  \includegraphics[width=10cm]{Rubik-doc-figF.pdf}
+%  \includegraphics[width=10cm]{rubik-doc-figF.pdf}
 % \else
 % \fi
 % \end{minipage}
@@ -118,58 +119,109 @@
 % The  \rubikcube\  package (part of the \textsc{rubik} `bundle') provides  a 
 % collection of \LaTeX\ commands 
 % and macros for  typesetting  Rubik cube  configurations  using the  
-% PGF/TikZ graphic languages. Note that this package relates  only to  the 
+% PGF/TikZ graphic languages, and relates  only to  the 
 % familiar  3x3x3 Rubik cube. 
-% We have extended  the  layer-rotation  hieroglyphic notation,  originally  
+% We have extended  the  rotation  hieroglyph notation,  originally  
 % developed  by Garfath-Cox (1981), and improved by Duvoid (2010, 2011).
 %
 % The \rubikcube\ package is designed to be  used in conjunction 
-% with the  \textsc{rubikrotation} package (see below); the former deals 
-% primarily with  typesetting, while the latter  processes  rotation sequences
-%  and keeps  track of the cube's configuration.
+% with both  the  \textsc{rubikrotation} package and the \textsc{rubikpatterns} package. 
+% The \rubikcube\ package deals  primarily with  typesetting, while the \textsc{rubikrotation}
+% package processes  rotation sequences  and keeps  track of the cube's configuration.
+% The \textsc{rubikpatterns} package is a small database of Rubik cube rotation sequences 
+% which generate well-known named cube configurations (patterns).
+% For full functionality it is  recommended that  all three Rubik packages  are used 
+% together; for~example,
+%\begin{verbatim}
+%  \usepackage{tikz,rubikcube,rubikrotation,rubikpatterns}
+%\end{verbatim}
+% Note that the \verb!TikZ! package must be loaded \textit{before} the \textsc{rubikcube} 
+% package.
 %
 %  The \rubikcube\ package has been road-tested  on a Microsoft 
-%  platform (with \textsf{MiK}\TeX), a Linux platform (Mandriva and {\TeX}Live),
-%  and on a Solaris platform (OpenIndiana).
+%  platform (with \textsf{MiK}\TeX), a GNU-Linux platform (Debian 8.2.0 
+%  and {\TeX}Live 2016), and on a Solaris platform (OpenIndiana).
 %
 % 
 % For the mathematics and group theory associated with the   Rubik cube  see Chen~(2004), 
-% Davis (2006), Golomb~(1981, 1982), Joyner~(2008), Hofstadter (1981), Hutchings~(2011), 
-% Kociemba web site, Rokicki~\textit{et al.} (2013), Tran~(2005).
-%  Useful web sites for solvers are the Speedsolving website, and  those 
-% maintained  by Duvoid,  by Fridrich, by Jelinek,  by Reid, and by Vandenburgh 
-% (see References).
+% Davis (2006), Golomb~(1981, 1982),  Hofstadter (1981), Hutchings~(2011), 
+% Heise website, Joyner~(2008), Kociemba website, 
+% Rokicki~\textit{et al.} (2013), Scherphius website,  Tran~(2005).
+%  Other useful websites are the Speedsolving website, and  those 
+% maintained  by Duvoid,  by Fridrich, by Jelinek,  by Reid, and by Vandenburgh. 
+%  A useful online solver utility (based on an algorithm by Kociemba) is
+% available at the RuWix website. Websites with good pages on  patterns and symmetries are 
+% those by  Fridrich, Kociemba, Longridge, Reid, Randelshofer, Scherphius 
+% (see References for details).
 %
 %
 %      \subsection{Requirements}
 %
-%  The \rubikcube\ package requires the TikZ package.
-%  In particular, we make  use the \cmd{\pgfmathsetmacro} command and 
-% the TikZ picture environment.
+%  The \rubikcube\ package requires the TikZ package, since it makes  
+%  use  of the TikZ picture environment and the \cmd{\pgfmathsetmacro} command.
+% Consequently, the \verb!TikZ! package must be loaded \textit{before} 
+% the \textsc{rubikcube}  package.
+%
+%  Both the \textsc{rubikrotation} and \textsc{rubikpatterns}  packages (see below) 
+% require  Perl to be installed.
 %
 %
 %  \subsection[rubikrotation package]{Supporting  tool---the 
 %   \textsc{rubikrotation} package}
-%  \label{sec:addons}
+%   \label{sec:rubikrotation}
 %
-%  The \textsc{rubikrotation} package, is a dynamic extension to
-% the \rubikcube\ package, and is part of the `Rubk bundle'. It consists of  the  
+%  The \textsc{rubikrotation} package (also part of the \textsc{rubik} `bundle'), 
+%  is a dynamic extension to  the \rubikcube\ package. It consists of  the  
 % Perl program  \texttt{rubikrotation.pl}  and the associated  style option
 %  \texttt{rubikrotation.sty}. 
-%  The \textsc{rubikrotation} package  implements rotation sequences and 
-%  random  scrambling of the 3x3x3 Rubik cube on-the-fly using a
+%  The \textsc{rubikrotation} package  implements rotation sequences on-the-fly using a
 %   \cmd{\RubikRotation}\marg{rotation-sequence} command. It returns the 
-% new state in a form which is then used by the \rubikcube\ package.
+%  new state in a form which can then be used by the \rubikcube\ package.
+% It also returns some useful strings associated with the rotation sequence 
+% which can  be used by the \rubikcube\ 
+% package---see also Section~\ref{sec:showsequence}.
 %
 %  Since the  \cmd{\RubikRotation} command works by \textsc{call}ing the  
 %  \texttt{rubikrotation.pl} program, it follows that the \textsc{rubikrotation}
 %   package requires  (a)~Perl to be installed, 
-%  and (b)~\LaTeX\ needs to be run using the  \texttt{--shell-escape} commandline option.
-%  See the \textsc{rubikrotation}  documentation for details.
+%  and (b)~the \LaTeX\ engine  needs to be run using the  \texttt{--shell-escape} 
+%  command-line option. Those wishing to use Lua\LaTeX\  will also need to have access 
+% to the recent \texttt{shellesc} package (in {\TeX}Live 2016). 
+% The \texttt{shellesc} package can always be downloaded from CTAN directly.
+%  See the \textsc{rubikrotation}  documentation for further details.
+%
+%
+%
+%  \subsection[rubikpatterns]{Supporting  database---\textsc{rubikpatterns.sty} }
+%  \label{sec:patterns}
+%
+%  
+%  The \textsc{rubikpatterns.sty} file (also part of the \textsc{rubik} `bundle')
+%  is a small database of some well-known  Rubik cube rotation sequences, stored as 
+%  named macros. For~example, the `fourspot' and `sixspot' sequences are encoded in 
+% this package as follows:
+%\begin{verbatim}
+%  \newcommand{\fourspot}{[fourspot],F2,B2,U,Dp,R2,L2,U,Dp,<(12q*, 8f*)>}
+%  \newcommand{\sixspot}{[sixspot],U,Dp,R,Lp,F,Bp,U,Dp,<(8q*, 8f*)>}
+%\end{verbatim}
+%  These sequences  can be  processed by name (using the  \cmd{\RubikRotation} command
+%  which also requires Perl to be installed---see Section~\ref{sec:rubikrotation}), and 
+% then displayed (using the \cmd{\ShowCube} command in conjunction with various 
+%  \cmd{\DrawRubikCube...} commands). So, for~example, one could typeset the so-called 
+%  `fourspot' configuration using the following code:
+%\begin{verbatim}
+%  \usepackage{tikz,rubikcube,rubikrotation,rubikpatterns}
+%  ...
+%  \RubikCubeSolved
+%  \RubikRotation{\fourspot}
+%  \ShowCube{2.4cm}{0.6}{\DrawRubikCubeRU}
+%\end{verbatim}
+% See also the \textsc{rubikrotation}  documentation---especially
+% Section~5.1.1 \textit{Sequences as macros}.
 %
 %
 %  \subsection{Copyright}
-%  Copyright 2014--2015 RWD Nickalls and A Syropoulos.
+%  Copyright 2014--2017 RWD Nickalls and A Syropoulos.
 %
 % \medskip
 % {\noindent}This work may be distributed and/or modified under the
@@ -181,31 +233,39 @@
 %
 % \section{Installation}
 %
+% The Rubik bundle consists of the three package \rubikcube, \textsc{rubikrotation} 
+% and \textsc{rubikpatterns}, each of which needs to be installed separately.
+% Here we describe  the installation of the \rubikcube\ package.
 %
-%  \subsection{Generating the files}
+%  \subsection{Generating the \rubikcube\ files}
 %
 %  Place the file \texttt{rubikcube.zip} into a temporary directory, and unzip it. 
 % This will generate the following files:
 %\begin{verbatim}
 %   rubikcube.ins
 %   rubikcube.dtx
-%   rubikcube.pdf
-%   Rubik-doc-figA.pdf
-%   Rubik-doc-figB.pdf
-%   Rubik-doc-figC.pdf
-%   Rubik-doc-figD.pdf
-%   Rubik-doc-figE.pdf
-%   Rubik-doc-figF.pdf
+%   rubikcube.pdf         --documentation of the rubikcube package
+%   rubik-doc-figA.pdf
+%   rubik-doc-figB.pdf
+%   rubik-doc-figC.pdf
+%   rubik-doc-figD.pdf
+%   rubik-doc-figE.pdf
+%   rubik-doc-figF.pdf
+%   rubikexamples.tex
+%   rubikexamples.pdf
+%   rubikexamples.sh
+%   rubikexamples.bat
 %\end{verbatim}
+%
 %  The  style option \texttt{rubikcube.sty} is generated by  running (pdf)\LaTeX\ on  
 % the file \texttt{rubikcube.ins}  as follows:
 %\begin{verbatim}
 %   pdflatex  rubikcube.ins 
 %\end{verbatim}
 % This documentation file (\texttt{rubikcube.pdf}) can then be generated using the following
-% steps\,\footnote{Since the documentation includes a complicated indexing 
-% system as well a \textsc{pdf} index and hyperef links (the package \texttt{hypdoc}
-% is used), then  several pdflatex runs are required. Prior to the first run it is
+% steps\,\footnote{Several pdflatex runs are required, since the documentation includes 
+% an index as well as hyperef links (the package \texttt{hypdoc}
+% is used). Prior to the first run it is
 % a good idea to delete any relevant \texttt{.toc}, \texttt{.aux}, \texttt{.out} files.}:
 %\begin{verbatim}
 %   pdflatex   rubikcube.dtx
@@ -216,6 +276,14 @@
 %   pdflatex   rubikcube.dtx
 %\end{verbatim}
 %
+% Note that the package includes a  `rubikexamples' file (\texttt{rubikexamples.tex})
+% as well as associated  \texttt{.sh} (Linux) and \texttt{.bat} (Microsoft) batch 
+% files which can be used to facilitate processing the file. 
+% Note that many of the examples in this file use the \cmd{\RubikRotation} command
+% (associated with the \textsc{rubikrotation} package), 
+% and hence this file needs to be run using the \verb!--shell-escape! command-line 
+% option  (see Section~\ref{sec:rubikrotation} for details).
+
 %
 %  \subsection{Placing the files}
 %
@@ -229,7 +297,7 @@
 %
 % \medskip
 % {\noindent}Finally, (depending on your system) update the  \TeX\ file database.
-% For example, on a Linux system one uses the  \texttt{texhash} command.
+% For~example, on a Linux system one uses the  \texttt{texhash} command.
 %
 %
 % \subsection{Usage}
@@ -240,212 +308,123 @@
 % \begin{quote}
 %\begin{verbatim}
 % \usepackage{tikz}
-% \usepackage{rubikcube,rubikrotation}
+% \usepackage{rubikcube,rubikrotation,rubikpatterns}
 %\end{verbatim}
 % \end{quote}
 % However, the \rubikcube\ package does check for the presence of TikZ, and will 
 % load it  if TikZ is not already loaded.
 % While \rubikcube\ is a stand-alone package, it is best to also load the complementary
-%  \textsc{rubikrotation}  package.
-%
-%
-%    \section{TikZ picture environment}
-%      \label{sec:tikz}
-%
-%  For a basic introduction to the use of TikZ see the following manuals
-%  (from CTAN or from \texttt{http://altermundus.com/}).
-%  \begin{itemize}
-%  \item \texttt{pgfmanual.pdf}, version 3.0.1a (August 2015) (1161 pages)
-%  \item \texttt{pgfplot.pdf}, version 1.12.1 (2015) (504 pages)
-%  \item tkz-base-screen.pdf
-%  \end{itemize}
-% An example of the TikZ picture environment for use with the \rubikcube\ package 
-% is as follows:  
-% \begin{quote}
-%\begin{verbatim}
-% \begin{tikzpicture}[scale=0.5]
-% ....
-% \end{tikzpicture}%
-%\end{verbatim}
-% \end{quote}
-% If no scale is used (default scale = 1), then each of the small
-% cubie sides  will have a length of 1~cm.
-%
-% A very useful feature of  TikZ  is that it automatically 
-% minimises the surrounding  white-space, and consequently this is 
-% mostly quite sufficient. However, it is good practice to place 
-% a \% symbol after the \verb!\end{tikzpicture}! command *see above) 
-% to avoid  additional white space (see Section~\ref{sec:trailingpercent}).
-%
-%
-%   \subsection[ShowCube command]{\cmd{\ShowCube} command}
-%   \label{sec:showcube}
-%
-% \DescribeMacro{\ShowCube}
-% \DescribeMacro{\ShowCubeF}
-% When making side-by-side figures it can be very helpful
-%  to place each sub-figure inside a  minipage.
-% In this case, a useful approach is to  first adjust 
-% the  tikzpicture `scale' parameter  to obtain the appropriate size, and 
-% then adjust the minipage width as necessary 
-% (see Section~\ref{sec:sizeofminipage}).
-% The  \cmd{\ShowCube} macro (See Section~\ref{sec:showcubecode}) places one 
-% or more commands  inside a tikzpicture environment  and places all of 
-% these inside a minipage.  It takes three arguments: the first is the 
-% minipage width (\verb!#1!), second is  the tikzpicture scale 
-% factor (\verb!#2!), and third is a \cmd{\Draw..} command (|#3|).
-% 
-% \noindent\textsc{usage}:
-% The following command would display a Rubik cube  in a 
-% minipage of  width 2cm  using a tikzpicture scale factor of 0.5:
-%\begin{verbatim}
-% \ShowCube{2cm}{0.5}{\DrawRubikCubeRU}
-%\end{verbatim}
-% For example, the following two sets of commands are equivalent (see
-%  Section~\ref{sec:showcubecode} for the code); i.e.,~any commands which are valid in
-% a \texttt{tikzpicture} environment may be used as the main argument for the 
-% \cmd{\ShowCube} command.
-% $$
-%   \left.
-%   \begin{array}{l} 
-%   \verb!\RubikCubeSolved!\\
-%   \verb!\begin{minipage}{2cm}!\\
-%   \ \   \verb!\centering!\\
-%   \ \   \verb!\begin{tikzpicture}[scale=0.5]!\\
-%   \ \ \ \ \   \verb!\DrawRubikCubeRU!\\
-%   \ \ \ \ \   \verb!\draw[->] (0.5,5) -- (0.5,4);!\\
-%   \ \   \verb!\end{tikzpicture}!\\
-%   \verb!\end{minipage}!\\
-%   \end{array}
-%         \right\}  
-%                 \begin{array}{l}  
-%                 \verb!\RubikCubeSolved!\\
-%                 \verb!\ShowCube{2cm}{0.5}{%!\\
-%                 \ \ \ \ \verb!\DrawRubikCubeRU!\\
-%                 \ \ \ \ \verb!\draw[->] (0.5,5) -- (0.5,4);!\\
-%                 \ \verb!}!\\
-%                 \end{array}
-% $$
-%
-% The  \cmd{\ShowCubeF} command is similar in all respects except that it places 
-% an fbox around the minipage in order to enable users to see the extent of any 
-% associated white space.
-%
-% Unexpected spacing between two adjacent images, or between an 
-% image and adjacent text, is usually related to 
-% `hidden' white-space associated with the image itself or excessive width 
-% of the associated \cmd{\minipage} (see also Section~\ref{sec:trailingpercent}).
-% Consequently,  a temporary fbox around the minipage can be a 
-% useful aid  when trying to  visualise the  full extent of the minipage 
-% (and its associated whitespace). Use the \cmd{\ShowCubeF} command for this, as follows:
-%
-% \medskip
-%
-% \RubikCubeSolved
-% \ShowCubeF{4cm}{0.3}{\DrawRubikCubeRU}
-%\begin{minipage}{5cm}
-%\begin{verbatim}
-% \ShowCubeF{4cm}{0.3}{\DrawRubikCubeRU}
-%\end{verbatim}
-%\end{minipage}
-%
-% \medskip
-% {\noindent}Clearly either the minipage is too wide (4cm) or the \texttt{tikzpicture} 
-% scale factor is too  small (0.3). Once the figure/code has been corrected, then the 
-% \texttt{F}  in  the  \cmd{\ShowCubeF} command  can be removed. Note that while 
-% the \cmd{\ShowCube} command centers  the image  inside the minipage, \LaTeX\ positions 
-% the minipage in the \cmd{\textwidth}, and  hence it is  generally best to minimise 
-% the white-space as revealed by the \cmd{\ShowCubeF}  command.  The relationship 
-% between the required width of the minipage and the TikZ  scale factor  for the various 
-% Rubik cube images is detailed in  Section~\ref{sec:sizeofminipage}.
+%  \textsc{rubikrotation} and \textsc{rubikpatterns}  packages.
 %
 %
+% \DescribeMacro{\rubikcube}
+% This command generates the logo \rubikcube.
 %
-%   \subsection[Draw.. error message]{\cmd{\Draw} error message}
-%   \label{sec:drawerrormessage}
 %
-% If a \rubikcube\   \cmd{\Draw..} command is used \textit{outside} a 
-% TikZ picture  environment, then \LaTeX\  issues an
-%  ``Undefined control sequence'' error message, indicating 
-% that it is trying to draw  something using an undefined 
-% TikZ \cmd{\draw} command. 
 %
-% For example, if we  use  the \rubikcube\ command 
-%  \cmd{\DrawRubikFlat}  without a surrounding TikZ picture environment 
-%  then something similar to  the following error message will be generated.
-%\begin{verbatim} 
-%! Undefined control sequence.
-%\DrawFlatUp ... }{#1}\pgfmathsetmacro {\uy }{#2}\draw
-%                                                      [line join=round,...
-%l.56 \DrawRubikFlat
-%\end{verbatim}
+%        \section{Command conventions}
+%        \label{sec:conventions}
 %
 %
+% All  \rubikcube\ package commands assume a 3x3x3 cube by default.
+% There are three primary command categories: (a)~\cmd{\Draw..} commands 
+% (which must always be used \textit{inside} a TikZ picture environment), 
+%  (b)~`parameter-allocation' commands---e.g.,~\cmd{\RubikCubeSolved}---which can 
+%  be used either inside or outside  a TikZ environment),  
+%  and (c)~commands which can be used in ordinary text 
+% (e.g.,~|\rr{}| rotation commands).
 %
-%        \section{Command conventions}
-%        \label{sec:conventions}
 %
-%   \subsection{Commands and  environments}
+%   \subsection{Environments}
 %
 % Although the \rubikcube\ package has been designed with TikZ in mind, 
-% it is important to appreciate that of all the  various \rubikcube\  
+% it is important to appreciate that of all the  various \rubikcube\ package   
 % commands only the Rubik \cmd{\Draw...} commands and  TikZ commands actually 
 % have to be  used  inside  a  TikZ picture environment. 
 %
-% Indeed, using  \rubikcube\  commands which influence the Rubik colour state
+% Indeed, using  \rubikcube\ package commands which influence the Rubik colour state
 % (configuration) outside the \texttt{tikzpicture}, \texttt{minipage} or 
 % \texttt{figure}  environments can make for useful 
 % flexibility when a document is generating  more than one figure
 % or image. This is because the scope of any colours specified by commands inside
 % these  environments is constrained to 
 % be `local' to that particular environment, and hence  any change in the 
-% Rubik colour state brought  about by such commands is not accessable 
+% Rubik colour state brought  about by such commands is not accessible 
 % globally (i.e.,~outside  the environment) ---see also Section~5 in the documentation 
 % of the \textsc{rubikrotation} package.
 %
 % Consequently users need to be mindful of the  environments when  
-% drawing long sequences of rotations across several figures; for example, keeping 
-% \cmd{\RubikRotation} commands outside the environments keeps their effects global. 
+% drawing  sequences of rotations across several figures; for~example, keeping commands like 
+% \cmd{\RubikRotation}, \cmd{\RubikFace..}, \cmd{\RubikSide..}, \cmd{\RubikCubeSolved}, 
+%  outside the environments keeps their effects global. 
+%
 %
 %   \subsection{Capital letters}
 %
-%  Each `word' in a command (except the word `text')  starts with a capital letter. 
-%  For example,  \cmd{\DrawRubikCubeRU}, \cmd{\DrawCubieRU}. 
-%  However, as with  \LaTeX,  `text..' commands start with a lowercase `t'; 
-%  for example \cmd{\textCubieRU}.  Letters  for  colours (R, O, Y, G, B, W, X)  are 
-%  always written in uppercase. 
+% Virtually all Rubik bundle commands start with a capital letter, primarily to 
+% avoid any confusion with TikZ commands (these generally start with lower-case letters). However,
+%  each `word' in a Rubik bundle  command (except the word `text') also starts 
+%  with a capital letter, primarily to facilitate readability. 
+%  For~example,  \cmd{\DrawRubikCubeRU}, \cmd{\DrawCubieRU}. 
+%  However, as with  \LaTeX,  `text..' commands start with a lower-case `t'; 
+%  for~example \cmd{\textCubieRU}.  Letter arguments  for  colours (R, O, Y, G, B, W, X)  are 
+%  always written in upper-case letters. 
+%
 %
 %
 %     \subsection{XYZ argument ordering}
+%     \label{sec:xyzarguments}
+%
+% Many commands have an appended two, three, or even six  ordered arguments or letters 
+% which form  some feature of the structure of a command; perhaps 
+%  either  face  or colour code or a viewpoint direction. 
 %
-% Many commands have an appended two (XY) or three (XYZ) ordered letter code 
-% which is used to for  specifying some feature of the command; perhaps 
-%  either  face or cubie colours or a viewpoint direction. 
+% We adopt the convention that where ordering of arguments is critical, then the 
+% arguments are ordered in the XYZ, $+$, $-$  order. An XYZ code implies that 
+% the first letter in the code relates to  an X-related parameter, 
+% for~example,  L (Left) or R (Right); the second letter relates to  a Y-related 
+% parameter,  for~example,  U (Up) or D (Down); the third (if required) 
+% relates to  a Z-related  parameter,  for~example,  F (Front) or B (Back)
+% ---see Figure~\ref{fig:notation}.
 %
-% The convention is that the letter codes are ordered in the XYZ order; 
-% i.e.,~the first code relates to  an X-related parameter; 
-% for example  L (Left) or R (Right); the second relates to  a Y-related 
-% parameter;  for example  U (Up) or D (Down); the third (if required) 
-% relates to  a Z-related  parameter;  for example  F (Front) or B (Back).
+% Some commands have six arguments which adopt an  (XYZ;$+$$-$) format. In this case,
+% for~example, the  \cmd{\SolvedConfig} command, for which   the six colour  arguments 
+% are ordered  as X$+$, X$-$,  Y$+$, Y$-$, Z$+$, Z$-$. Here the colour argument 
+% associated with a  face positioned on the $+$ve axis is  ordered before  
+% its $-$ve  complement on the same axis. 
 %
+% Another example is the  |\DrawCubieRU{G}{Y}{O}| command, which  draws a cubie. Here 
+% the RU letters are XY ordered; i.e.,~RightUp viewpoint. The sequence of  colour codes 
+% for the three visible  faces are XYZ ordered, and hence result in the cube having a 
+% Green Right face,  Yellow Up face and Orange Front face.
 %
-% \textsc{example}: |\DrawCubieRU{G}{Y}{O}|  draws a cubie from 
-% the RightUp viewpoint. The sequence of  colour codes for the three visible 
-% faces are XYZ ordered, and hence result in the cube having a Green Right face, 
-% Yellow Up face and Orange Front face.
 %
 %
 %  \subsection{Trailing \% on the end of commands}
 % \label{sec:trailingpercent}
 %
-% It is important to include a trailing \% on the end of \rubikcube\ 
-% commands when used \textit{outside}  a TikZ picture environment, and 
-% also on the end of each \cmd{\end\{tikzpicture\}} environment command. 
-% This is to prevent  unwanted `space' characters appearing in 
-% the graphics. In \TeX\ every newline character is automatically converted
+% Since the all the output of this package is drawn using graphic elements
+% using TikZ, it is important to include a trailing \% on the end 
+% of \rubikcube\ package commands when used \textit{outside}  a TikZ picture environment, and 
+% also on the end of the \cmd{\end\{tikzpicture\}} environment command itself. 
+% In particular it is  important to use a trailing \% on 
+% the end of lines which  break  before the terminal curly bracket of a \cmd{\newcommand}.
+%
+% This is to prevent accumulating spurious spaces which may otherwise appear in 
+% figures and diagrams as a strange or unexpected horizontal shift or white-space.
+% That this can occur is because in \TeX\ every newline character is automatically converted
 %  to a white space---unless you have an empty line 
-% (Feuers\"{a}nger 2015, \S\,3.2.3, page~20). 
+% (Feuers\"{a}nger 2016). 
+%
+% The \LaTeX\  fbox is a useful aid for visualising unwanted white space 
+% which may have accumulated, and for identifying the cause. 
+% See  Section~\ref{sec:showcube} on the \cmd{\ShowCubeF} command for 
+% more regarding this approach.
 %
+% Although this effect is mostly small, and  is generally only observed in situations
+% when centering a graphic is critical, it is, however, cumulative and can be surprisingly large. 
+% In these situations,  the cure is the addition of terminal \%  characters to preceding 
+% code guided by careful detective use of the fbox technique mentioned above.
 %
 %
 %     \subsection{Cubies, cubicles, faces and facelets}
@@ -457,38 +436,283 @@
 %
 % We distinguish three types of cubie:  
 % centre-cubies (single colour), edge-cubies (two colours) and corner-cubies 
-% (three colours). For example, the red/white edge-cubie  is called  
+% (three colours). For~example, the red/white edge-cubie  is called  
 % the RW cubie, and  the red/white/green corner-cubie  is called the 
 % RWG cubie etc. Note that the colour of a particular face of a  3x3x3 Rubik 
 % cube is determined by the colour of its  centre-cubie. 
 %
 % Similarly, the positions (known as `cubicles') occupied by cubies  are 
-% defined using either a  two or three  letter face  code. For example the  
+% defined using either a  two or three  letter face  code. For~example, the  
 % right edge position  in the Up-layer is termed  the  Up/Right position, 
 % or just the UR position, and the  corner   joining the \textsc{down}  
 % \textsc{front} and \textsc{right} faces is the DFR position.    
 %
 %
 %
-%    \section{Colours}
+%     \section{Rubik cube coordinates}
+%     \label{sec:coordinates}
+%
+% The coordinate origin  of all 2D  Rubik cube images  is located  
+% at the bottom-left corner of the \textsc{front} face, as shown in 
+%  Figure~\ref{fig:cubesquaregraph}. Note also that the bottom left 
+%  extent  of this particular  2D  rendering of the cube  is actually  at $(-1,-1)$, 
+%  and hence the default height and width of all oblique-view cubes is 4~units
+%  (i.e.,~equivalent to 4cm if the TikZ scale-factor = 1). 
+%
+% \begin{figure}[hbt]
+% \centering
+% \ifpdf
+%   \includegraphics[height=4cm]{rubik-doc-figB.pdf}
+% \else
+% \includegraphics[height=4cm]{rubik-doc-figB.eps}
+% \fi
+%
+% \parbox{9cm}{\caption{\label{fig:cubesquaregraph}Origin of coordinates 
+%  is at the  bottom left corner of the grey \textsc{front} face. 
+%  Since  $P$ is  at $(-1,-1)$ then the default height and width of the 
+%  2D~cube image is 4~units.}}
+% \end{figure}
+%
+% Arranging for $P$ to be at $(-1,-1)$, as well as using the bottom-left corner 
+% of the \textsc{front} face as  the origin, are useful  design  
+% features which make it easy to know the coordinates of any point, and hence 
+% facilitate the use any of the  TikZ commands  
+% (e.g.,~\cmd{\draw} and \cmd{\node} commands) to  superimpose lines, 
+% arrows and text etc.,~onto the Rubik cube (see Section~\ref{sec:arrows}).
+
+%
+%      \subsection[Size of cube minipage]{Size of cube \cmd{\minipage}}
+%      \label{sec:sizeofminipage}
+%
+%  Since the the default height and width of the oblique 2D~cube image is 
+% 4~units (see Section~\ref{sec:coordinates} above), 
+%  it follows that the width of the \cmd{\minipage} required for a cube in a 
+%  \texttt{tikzpicture}  environment can be easily calculated. For~example, 
+%  if the \texttt{tikzpicture} scale factor used is $0.5$, then the minimum
+%  width of the required minipage for the \cmd{\DrawRubikCubeLD} view (shown above)
+%  is therefore $0.5 \times 4\mbox{cm} =  2\mbox{cm}$. 
+%
+% Note that the width of the semi-flat (SF) cube representation is therefore 
+% 10~units ($=3+3+1+3$),  and that of the  flat (F) cube is 12~units ($=3+3+3+3$)
+%  --- see Section~\ref{sec:flatcommands} for images of these forms. 
+% If in doubt check the  horizontal extent of an image  using the \cmd{\ShowCubeF} command,
+% which places an fbox around the image.
+%
+%
+%
+%    \section{TikZ picture environment}
+%      \label{sec:tikz}
+% 
+%  All the Rubik bundle \cmd{\Draw..} commands are designed to be used 
+% with the TikZ picture environment, and  are compatible with standard TikZ. 
+%  For a basic introduction to the use of TikZ see the following manuals
+%  (from CTAN or from \texttt{http://altermundus.com/}).
+%  \begin{itemize}
+%  \item \texttt{https://en.wikipedia.org/wiki/PGF/TikZ}
+%  \item \texttt{pgfmanual.pdf}, version 3.0.1a (?\,2013) (1161 pages)
+%  \item \texttt{pgfplot.pdf}, version 1.13 (2016) (544 pages)
+%  \item \texttt{tkz-base-screen.pdf}, version 1.16c (2011) (91 pages)
+%  \end{itemize}
+% An example of the TikZ picture environment for use with the Rubik bundle 
+% is as follows:  
+% \begin{quote}
+%\begin{verbatim}
+% \begin{tikzpicture}[scale=0.5]
+% ...
+% \end{tikzpicture}%
+%\end{verbatim}
+% \end{quote}
+% If no scale-factor is used (default scale-factor = 1), then each of the small
+% cubie sides  will have a length of 1~cm.
+%
+% \textsc{useful commands}:\  Probably the most  
+% useful TikZ commands for use with regard 
+% to the Rubik bundle are the \cmd{\draw} command (for drawing  lines, arrows, circles), 
+% and the \cmd{\node} command (for writing text at specific coordinate locations). 
+% The basic structure of these commands  is as~follows, where 
+% (x,y) represent grid coordinates of start or end points of lines or arrows, 
+% or of a circle centre, or of text position (see Sections~\ref{sec:flatcommands} 
+% and \ref{sec:arrows} for examples).
+% \begin{quote}
+% \begin{verbatim}
+% \draw[->,thick,color=blue] (4.5, 2.5) -- (3.5,2.5);
+% \draw[->,ultra thick,color=red] (4.5, 2.5) -- (3.5,2.5);
+% \draw [color=blue, thick] (0.3, 0.3)  circle (1.3);
+% \node (B) at (7.5, 1.5)   [black]{\small\textsf{B}};
+%\end{verbatim}
+%\end{quote}
+% Remember that all TikZ commands  which are valid inside a \texttt{tikzpicture}
+% environment require a terminal semicolon (see Section~\ref{sec:arrows} 
+% for examples).
+%
+% \textsc{colours}: \ 
+% The following colors are predefined by TikZ: red, green, blue, cyan, magenta, 
+% yellow, black, gray, darkgray, lightgray, brown, lime, olive, orange, pink, 
+% purple, teal, violet and white (see \texttt{https://en.wikipedia.org/wiki/PGF/TikZ}).
+%
+% \textsc{line width}: \
+%  TikZ allows line width to be specified directly 
+% (e.g.,~\texttt{[line width=<dimension>]}), or by using the following abbreviations: 
+%  `ultra thin' for 0.1pt,  `very thin' for 0.2pt, `thin' for 0.4pt (the default width), 
+% `semi thick' for 0.6pt, `thick' for 0.8pt, `very thick' for 1.2pt, 
+% `ultra thick' for 1.6pt (see \texttt{https://en.wikipedia.org/wiki/PGF/TikZ}).
+%
+%% \textsc{white space}: \ 
+% A particularly useful feature of  TikZ  is that it automatically 
+% minimises any horizontal white-space. However, it is good practice to place 
+% a \% symbol after the \verb!\end{tikzpicture}! command *see above) 
+% to avoid  additional white space inadvertently being added by \LaTeX\
+%  (see Section~\ref{sec:trailingpercent}).
+%
+% When making images it can be helpful to place them inside a  minipage 
+% (e.g.,~using the  \cmd{\ShowCube}  command / environment below).
+% A~convenient approach is to  first adjust  the  value of the  tikzpicture scale-factor
+%  (to obtain the appropriate size), and  then adjust the minipage-width as necessary, using
+% the fbox associated with the \cmd{\ShowCubeF} command  
+% (see Section~\ref{sec:sizeofminipage} for a useful guide on this).
+%
+%  The main `display' tool for  drawing cubes is the \cmd{\ShowCube} command 
+% (see below), and this  incorporates a 
+% TikZ picture environment inside a minipage. The equivalent tool for 
+% displaying rotation sequences is the \cmd{\ShowSequence} command.
+% 
+%
+%
+%
+%
+%   \section[ShowCube command]{\cmd{\ShowCube} command}
+%   \label{sec:showcube}
+%
+%
+% \DescribeMacro{\ShowCube}
+% This command  \cmd{\ShowCube}\marg{width}\marg{scale-factor}\marg{commands}
+% is a convenient tool  which places one  or more commands  inside a 
+% tikzpicture environment  and places  all of  these inside a minipage
+% (see Section~\ref{sec:showcubecode} for the code).
+% This command takes three arguments: the first (\verb!#1!) is the  minipage width, 
+% the second (\verb!#2!) is  the tikzpicture scale  factor, and the third (\verb!#3!) 
+% is a  series of any \rubikcube\ package  \cmd{\Draw..}  and other commands, as well as 
+% any TikZ commands which are valid in  a \texttt{tikzpicture} environment 
+% (e.g.,~\cmd{\draw} or \cmd{\node}  etc.). 
+% 
+% \medskip
+% 
+% \noindent\textsc{usage}:
+% The following \cmd{\ShowCube} command  displays a Rubik cube 
+% (the `SixT's configuration\footnote{The \cmd{\sixts} macro is from the \textsc{rubikpatterns}
+% package.})  and a blue arrow  in a  minipage of  width~3cm,  using a tikzpicture scale 
+% factor of~0.5.
+% Note that the  TikZ  \cmd{\draw} command requires a terminal 
+% semicolon---see Section~\ref{sec:tikz}.
+% 
+% \medskip
+%
+% {\noindent}%
+% \begin{minipage}{6.6cm}
+%\begin{verbatim}
+% \RubikCubeSolved
+% \RubikRotation{\sixts}
+% \ShowCube{3cm}{0.5}{%
+%     \DrawRubikCubeLU
+%     \draw[->,thick,color=blue] (4.5, 2.5) -- (3.5,2.5);
+%      }
+%\end{verbatim}
+% \end{minipage}
+% \hspace{2.5cm}%
+%\RubikFaceUp{Y}{Y}{W}{W}{W}{W}{Y}{Y}{W}%
+%\RubikFaceDown{Y}{W}{W}{Y}{Y}{Y}{Y}{W}{W}%
+%\RubikFaceLeft{B}{G}{G}{B}{B}{B}{B}{G}{G}%
+%\RubikFaceRight{G}{B}{B}{G}{G}{G}{G}{B}{B}%
+%\RubikFaceFront{O}{O}{O}{R}{O}{R}{R}{O}{R}%
+%\RubikFaceBack{O}{R}{O}{O}{R}{O}{R}{R}{R}%
+% \ShowCube{3cm}{0.5}{%
+%     \DrawRubikCubeLU
+%     \draw[->,thick,color=blue] (4.5, 2.5) -- (3.5,2.5);
+%      }
+%
+% \medskip
+%
+% {\noindent}The convenience of the \cmd{\ShowCube} command  is illustrated below; the 
+%  \cmd{\ShowCube} command on the left is equivalent to the bunch of commands
+%  on the right (see Section~\ref{sec:showcubecode} for the  complete code).
+% $$
+%  \left.  
+%    \begin{array}{l}
+%    {\ }\\
+%    {\ }\\
+%    \verb!\ShowCube{3cm}{0.5}{...}!\\
+%    {\ }\\
+%    {\ }\\
+%    \end{array}
+%   \right\{       
+%          \begin{array}{l} 
+%          \verb!\begin{minipage}{3cm}%!\\
+%          \verb!\centering%!\\
+%          \verb!\begin{tikzpicture}[scale=0.5]!\\
+%          ...\\
+%          \verb!\end{tikzpicture}%!\\
+%          \verb!\end{minipage}%!\\
+%          \end{array}
+% $$
+%
+% \DescribeMacro{\ShowCubeF}
+% The  \cmd{\ShowCubeF} command is similar in all respects except that it places 
+% an fbox around the minipage in order to enable users to see the extent of any 
+% associated white space. For~example, unexpected spacing between two adjacent images, 
+% or between an  image and adjacent text, is usually related to 
+% `hidden' white-space associated with the image itself or excessive width 
+% of the associated \cmd{\minipage} (see also Section~\ref{sec:trailingpercent}).
+% Consequently,  a temporary fbox around the minipage can be a 
+% useful aid  when trying to  visualise the  full extent of the minipage 
+% (and its associated white-space). Use the \cmd{\ShowCubeF} command for this. 
+
+% For~example, the following use of the \cmd{\ShowCubeF} command reveals a significant 
+% white-space problem:
+%
+% \medskip
+%{\noindent}%
+%\begin{minipage}{6.6cm}
+%\begin{verbatim}
+% \ShowCubeF{4cm}{0.3}{\DrawRubikCubeRU}
+%\end{verbatim}
+%\end{minipage}
+% \RubikCubeSolved
+% \ShowCubeF{4cm}{0.3}{\DrawRubikCubeRU}
+%
+% \medskip
+% {\noindent}In this example, clearly either the minipage is too wide (4cm) or the \texttt{tikzpicture} 
+% scale factor is too  small (0.3). Once the figure/code has been corrected, then the 
+% \texttt{F}  in  the  \cmd{\ShowCubeF} command  can be removed. 
+%
+% Note that while the \cmd{\ShowCube} command centres  the image  
+% inside the minipage, \LaTeX\ positions 
+% the minipage in the \cmd{\textwidth}, and  hence it is  generally best to minimise 
+% the white-space as revealed by the \cmd{\ShowCubeF}  command.  The~relationship 
+% between the required width of the minipage and the TikZ  scale factor  for the various 
+% Rubik cube images is detailed in  Section~\ref{sec:sizeofminipage}.
+%
+%
+%
+%    \section{Colour commands}
+%      \label{sec:colours}
 %
 % The \rubikcube\ package uses seven colours which are defined as follows: 
-% red~(R), orange~(O), yellow~(Y),  green~(G), blue~(B),  white~(W), 
-% and   grey~(X). Now  according to the following webpage\,\footnote{We thank Peter Bartal  
-% for bringing this to our attention.}
+% R~(red), O~(orange), Y~(yellow),  G~(green), B~(blue),  W~(white), 
+% and   X~(grey). Now  according to the following webpage\,\footnote{We thank Peter Bartal  
+% for bringing this webpage to our attention.} 
 %
 % \medskip
 % \noindent\texttt{http://The-Rubiks-Cube.deviantart.com/journal/Using-Official-Rubik}
-% \newline\texttt{-s-Cube-Colors-268760351}
+% \newline\texttt{-s-Cube-Colors-268760351} (Nov 2011)
 %
 % \medskip
 % {\noindent}the official Rubik cube colours are defined as
 % \begin{quote}
 %\begin{verbatim}
-% .... colours which are red (PMS 200C*), green (PMS 347C*),
+% ... colours which are red (PMS 200C*), green (PMS 347C*),
 % blue (PMS 293C*), orange (PMS 021C*), yellow (PMS 012C*)
 % and white.
-% .....
+% ...
 % Pantone colors can not be accurately converted to RGB colors, 
 % the colors the web runs on. But they can be approximated. 
 % Through some research, I have found some estimations which 
@@ -512,10 +736,13 @@
 %\end{verbatim}
 % \end{quote}
 %  However, we have optimised these prescribed colours very slightly 
-%  for screen \& print use (for example, the yellow  was made very 
+%  for screen \& print use (for~example, the yellow  was made very 
 %  slightly brighter),  and so the actual colours implemented by 
-%  the \rubikcube\ package  are as follows 
-% (see Section~\ref{sec:codecolours}):
+%  the \rubikcube\ package  are as follows:\,\footnote{Although the Pantone
+%  colours cannot be converted to RGB, there is a subset of of Pantone colours
+%  which can be be converted using CMYK 
+%  (see \texttt{https://en.wikipedia.org/wiki/Pantone})}. 
+%  (see Section~\ref{sec:codecolours}):
 %
 % \begin{quote}
 %\begin{verbatim}
@@ -529,8 +756,8 @@
 %\end{verbatim}
 % \end{quote}
 % Different colours  can be allocated   to  the ROYGBWX letters  (using the 
-% \cmd{\colorlet} command) as required. For example, the standard `red' 
-% colour could  be allocated to the letter R using the command
+% standard \LaTeX\ \cmd{\colorlet} command) as required. For~example, the 
+% standard `red'  colour could  be allocated to the letter R using the command
 % \begin{quote}
 %    \cmd{\colorlet\{R\}\{red\}}
 % \end{quote}
@@ -543,140 +770,495 @@
 %     \subsection{Colour state of the cube}
 %     \label{sec:colourstate}
 %
+%
+%  \DescribeMacro{\RubikFace..}
+%  \DescribeMacro{\RubikSlice..}
+%  \DescribeMacro{\RubikSide..}
+%  \DescribeMacro{\RubikCubeSolved}
+%  \DescribeMacro{\RubikCubeGrey}
+%  \DescribeMacro{\RubikCubeGreyAll}
 % Initially, when \LaTeX\ reads the file \texttt{rubikcube.sty} all facelets
-% are allocated the code X, which can be regarded as a zero-colour state. 
-% Until a facelet is allocated  one of the six  Rubik colours it will be  rendered as
-%   grey  by a command  which just draws the current colour state of the cube or  a face 
-%  (e.g.,~\cmd{\DrawFlatUpSide}).
+% are allocated the colour-code X, which can be regarded as a zero-colour state. 
+% Until a facelet is allocated  one of the six   Rubik colours (using a suitable command)
+% it will be  rendered as  grey by a Rubik \cmd{\Draw...} command, since these commands 
+%  simply implement the current  colour state of the cube (e.g.,~\cmd{\DrawRubikCubeRU}).
 %
 % It is important to appreciate that the various commands which typeset faces 
 % or facelets with colours  differ in whether  they derive the colours
 % from the current internal colour `state' (configuration) of the Rubik cube, or not. 
+%
+% The colour state of cubies in faces and slices can be allocated using  \cmd{\RubikFace...}, 
+% \cmd{\RubikSlice...} and \cmd{\RubikSide...} commands (see Sections~\ref{sec:facecommands}, 
+% \ref{sec:slicecommands} and \ref{sec:rubikside}).  
+% In addition. the command \cmd{\RubikCubeSolved}, allocates  a prescribed  colour state 
+% for the whole `solved' cube, and is a very useful starting 
+% point (configuration) for subsequent rotations.
+% The commands \cmd{\RubikCubeGrey} and  \cmd{\RubikCubeGreyAll}   allocate  different colour 
+% states for the whole cube, and are designed to be useful starting points when illustrating
+% aspects of how to solve the cube. These two commands accept both `grey' and `gray' 
+% (to be consistent with TikZ).
+% Cubies  retain their colour allocation even if the cubies are moved using  
+% the \cmd{\RubikRotation} command (\textsc{rubikrotation} package), unless they are 
+% overwritten by a subsequent colour allocation command.
+%
+% To  visualise the current state of the cube one has to use a Rubik \cmd{\Draw...} command.
+% Although some \cmd{\Draw...} commands (e.g.,~\cmd{\DrawRubikLayerFace...}) allow
+%  you  to specify colours as arguments, \cmd{\Draw...} commands really only
+%  `paint' colours onto  cubie positions  (on the page, so to speak). 
+% \cmd{\Draw..} commands  never influence the internal Rubik  colour state.
+%
+% The current colour state / configuration of the Rubik cube can  be saved and 
+%  written to a named file (using the  \cmd{\SaveRubikState} command) in a form 
+% which can then be easily \cmd{\input} and processed  when required. 
+
+%
+%  \subsection{RubikFace commands}
+%   \label{sec:facecommands}
+%
+%  \DescribeMacro{\RubikFaceUp}
+%  \DescribeMacro{\RubikFaceDown}
+%  \DescribeMacro{\RubikFaceLeft}
+%  \DescribeMacro{\RubikFaceRight}
+%  \DescribeMacro{\RubikFaceFront}
+%  \DescribeMacro{\RubikFaceBack}
+% These  commands take nine colour arguments and  allocate   colours to the 
+% individual cubies  of a  Rubik cube face.
+% The ordering is isomorphic to the sequence 1--9, i.e.,~numbering the small 
+% squares 1-3~(top row, left to right), 4-6~(middle row, left to right), 
+% 7-9~(bottom row, left to right), as follows:
+% \begin{quote}
+% \fbox{
+% \begin{minipage}{1.6cm}
+% \#1 \#2 \#3 
+%
+% \#4 \#5 \#6
+%
+% \#7 \#8 \#9
+% \end{minipage}
+% }
+% \end{quote}
+% Conveniently, \LaTeX\ allows the colour arguments to be separated by spaces 
+% (e.g.,~separated in groups of three), or even spread across several 
+% lines (e.g.,~in a square block to resemble a 9-face). This is fortunate, as it
+%  allows the command to be formulated in a  visually intuitive way, as in the 
+% following examples.
+%
+% \begin{quote}
+% \begin{minipage}{8cm}
+%\begin{verbatim}
+% \RubikFaceUp{G}{B}{G}   {G}{W}{O}   {G}{O}{G}
+%
+% \RubikFaceFront{O}{W}{R}
+%                {W}{W}{W}
+%                {G}{W}{G}
 % 
-% The colour state of cubies in faces and slices can be allocated using  \cmd{\RubikFace...} 
-% and \cmd{\RubikSlice...} (see Sections~\ref{sec:facecommands} and \ref{sec:slicecommands}).
-% The commands \cmd{\RubikCubeSolved} and \cmd{RubikCubeGrey} allocate the colour state
-% for the whole cube, and are useful starting points for subsequent rotations. 
-% Note that cubies will retain their colour allocation even if the cubies are are moved by 
-% rotation commands, unless they are overwritten by a subsequent colour allocation command.
-% To  then visualise the cube one has to use a \cmd{\Draw...} command.
-%
-% The \textsc{rubikrotation} package keeps track of the Rubik state following
-% rotations and sequences of rotations processed by its \cmd{\RubikRotation} command.
-% The current colour state of the Rubik cube can be saved and  written to a named file 
-% using its  \cmd{\SaveRubikState} command; this file can then be \cmd{\input}  when required. 
-%
-% Note that although some \cmd{\Draw...} commands (e.g.,~\cmd{\DrawRubikLayerFace...}) use 
-% colours as arguments, these commands really only  `paint' colours onto  cubie positions 
-% (on the page, so to speak); i.e.,~these commands do not update the internal Rubik 
-% colour state, and hence  these colours do not  exist outside  the particular
-%  \texttt{tikzpicture} environment the \cmd{\Draw..} command was used in.
+%\end{verbatim}
+% \end{minipage}
+% \end{quote}
 %
+%  \DescribeMacro{\RubikFaceUpAll}
+%  \DescribeMacro{\RubikFaceDownAll}
+%  \DescribeMacro{\RubikFaceLeftAll}
+%  \DescribeMacro{\RubikFaceRightAll}
+%  \DescribeMacro{\RubikFaceFrontAll}
+%  \DescribeMacro{\RubikFaceBackAll}
+% Each of the above commands has an associated 
+% `\texttt{All}' version which allocates  the same colour to all the cubies 
+% on a 9-face  (i.e.,~only a single colour argument is required).
 %
-%     \section{Rubik cube coordinates}
-%     \label{sec:coordinates}
+% If you want a particular face to be all grey, then 
+%  use  the colour-code~X;  for~example,  \cmd{\RubikFaceUpAll\{X\}}.
+% Failure to include a valid colour argument  will generate a 
+% `missing parameter' error, and no colour will be 
+% allocated (i.e.,~you will see  a black-hole).
+% Use of these commands is shown in the following figure.
 %
-% The coordinate origin  of each view of the Rubik cube  is located  
-% at the bottom-left corner of the \textsc{front} face, as shown in 
-%  Figure~\ref{fig:cubesquaregraph}. Note also that the bottom left 
-%  corner of the cube  itself is at $(-1,-1)$, 
-%  and hence the default height and width of the cube is 4cm. 
+% \bigskip
+% 
+% \begin{minipage}{2.8cm}
+% \RubikFaceUpAll{X}
+% \RubikFaceRightAll{R}
+% \RubikFaceFront{W}{Y}{G}
+%                {W}{Y}{G}
+%                {W}{Y}{G}
+% \begin{tikzpicture}[scale=0.7]
+% \DrawRubikCubeRU
+% \end{tikzpicture}%
+% \end{minipage}
+%    \hspace{5mm}
+% \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+% \RubikFaceUpAll{X}
+% \RubikFaceRightAll{R}
+% \RubikFaceFront{W}{Y}{G}
+%                {W}{Y}{G}
+%                {W}{Y}{G}
+% \ShowCube{3cm}{0.7}{\DrawRubikCubeRU}
+% \end{verbatim}
+% \end{minipage}
+% 
 %
-% Using the \textsc{front} bottom-left corner as the origin
-% is an important feature since knowing the location of the 
-% origin enables one to easily use any of the  TikZ commands
-% (e.g.,~\cmd{\draw} and \cmd{\node} commands) to  superimpose lines, 
-% arrows and text etc.\ onto the Rubik cube (see Section~\ref{sec:arrows}).
+%       \subsection{Solved Configuration}
+%       \label{sec:solvedconfig}
 %
-% \begin{figure}[hbt]
+%  \DescribeMacro{\SolvedConfig}
+% This command  allocates  the six face colours according to the following ordered 
+% XYZ$+-$  argument rule, namely X$+$, X$-$, Y$+$, Y$-$, Z$+$, Z$-$; i.e.,~the order 
+% of the six colour arguments follows the face order
+% \textsc{right, left, up, down, front, back} (for notation see  
+% Section~\ref{sec:xyzarguments}  and Figure~\ref{fig:notation}). 
+% {\newline}\textsc{usage}:\ \verb!\SolvedConfig{G}{B}{W}{Y}{O}{R}!
+% {\newline}Examples of its use are shown in the  next section.
+%
+%
+%       \subsection{RubikCubeSolved command}
+%       \label{sec:rubikcubesolved}
+%
+%  \DescribeMacro{\RubikCubeSolved}
+%  \DescribeMacro{\RubikCubeSolvedWY}
+% The action of both of these  commands is identical: 
+% they both  set all the face colours to the following  standard `solved' cube
+% configuration, namely  Up=white, Down=yellow, Right=green, Left=blue, Front=orange, Back=red,
+% by invoking the above \cmd{\SolvedConfig} command,  as follows:
+%\begin{verbatim}
+%\newcommand{\RubikCubeSolved}{\SolvedConfig{G}{B}{W}{Y}{O}{R}}
+%\end{verbatim}
+% Note that this is in fact just a convenient short-hand for the following:
+%\begin{verbatim}
+%\newcommand{\RubikCubeSolved}{%
+%  \RubikFaceRightAll{G}%
+%  \RubikFaceLeftAll{B}%
+%  \RubikFaceUpAll{W}%
+%  \RubikFaceDownAll{Y}%
+%  \RubikFaceFrontAll{O}%
+%  \RubikFaceBackAll{R}%
+%}
+%\end{verbatim}
+% Note that for convenience, this configuration is also available using the command
+% \verb!\RubikCubeSolvedWY! (WY denoting White opposite Yellow).
+% This solved configuration is shown in the following 
+% semi-flat (SF) image.
+%
+%
+% \bigskip
+%
+% \begin{minipage}{5cm}
 % \centering
-% \ifpdf
-%   \includegraphics[height=3cm]{Rubik-doc-figB.pdf}
-% \else
-% \includegraphics[height=3cm]{Rubik-doc-figB.eps}
-% \fi
+% \begin{tikzpicture}[scale=0.5]
+% \RubikCubeSolvedWY
+% \DrawRubikCubeSF
+% \end{tikzpicture}%
+% \end{minipage}
+% \begin{minipage}{0.5\textwidth}
+%\begin{verbatim}
+%  \RubikCubeSolvedWY
+%  \ShowCube{5cm}{0.5}{\DrawRubikCubeSF}
+%\end{verbatim}
+% \end{minipage}
 %
-% \parbox{9cm}{\caption{\label{fig:cubesquaregraph}Origin of coordinates 
-%  is at the  bottom left corner of the grey \textsc{front} face. 
-%  The bottom left corner of the cube  itself is at $(-1,-1)$, 
-%  and hence the default height and width of the 3D-cube is 4cm.}}
-% \end{figure}
+% \bigskip
 %
+% Note that the width of the minipage  used in \cmd{\ShowCube} command above  
+% is set to 5cm. This value is derived from the fact 
+% that  the \textit{unscaled} width of the semi-flat image is 10cm (9 + 1 squares), and hence if
+% the TikZ scale factor is set to 0.5 then the minimum minipage width = $10 \times 0.5 = 5$cm
+% (see Section~\ref{sec:coordinates} for details).
 %
 %
-%      \subsection[Size of cube minipage]{Size of cube \cmd{\minipage}}
-%      \label{sec:sizeofminipage}
+% \textbf{Other orientations:} If other orientations of the solved cube are required, 
+% this can be easily achieved using the \cmd{\RubikRotation} command 
+% (from the \texttt{RubikRotation} package) to rotate the cube as required.
+% For~example, we could make a command to show the above solved cube upsidedown 
+% and rotated slightly, as follows:
+%\begin{verbatim}
+%\newcommand{\CubeUpSideDown}{\RubikCubeSolved\RubikRotation{x2,y}}
+%\end{verbatim}
+% ---this uses  the rotations \rrx, \rrx, to invert, and then  \rry\ to turn 
+% the cube 90~$\deg$:
 %
-%  Since the the default height and width of the 3D-cube is 4cm (see above), 
-%  it follows that the width of the \cmd{\minipage} required for a cube in a 
-%  \texttt{tikzpicture}  environment can be easily calculated. For example, 
-%  if the \texttt{tikzpicture} scale factor used is $0.5$, then the minimum
-%  width of the required minipage for the \cmd{\DrawRubikCubeLD} view (shown above)
-%  is therefore $0.5 \times 4\mbox{cm} =  2\mbox{cm}$. 
+% \bigskip
+%
+% \begin{minipage}{2.6cm}
+% \centering
+% \begin{tikzpicture}[scale=0.5]
+% \DrawNCubeAll{3}{O}{Y}{G}
+% \end{tikzpicture}%
+% \end{minipage}
+%    \hspace{5mm}
+% \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+% \CubeUpSideDown
+% \ShowCube{2cm}{0.5}\DrawRubikCubeRU}
+%\end{verbatim}
+% \end{minipage}
+%
+% \bigskip
+%
+%%  \DescribeMacro{\RubikCubeSolvedWB}
+%  \textbf{Other configurations:} While the `solved' WY colour configuration 
+% described above (White face opposite Yellow) 
+% is that of the most commonly occurring  Rubik cube, another  `solved' colour configuration
+% which is also commercially available has the White opposite Blue configuration, which 
+% is available  using the command \verb!\RubikCubeSolvedWB!.
+% Its  colour configuration is as follows:
+%
+%\begin{center}
+% \RubikCubeSolvedWB
+% \ShowCube{4cm}{0.4}{\DrawRubikCubeSF}%
+%\end{center}
+%
+% \bigskip
+%
+% Note that  users can easily create their own alternative `solved'  
+% face/colour versions.
+% For~example, the above mentioned  white opposite
+% blue~(WB)  solved configuration  command \verb!\RubikCubeSolvedWB!  
+% (white opposite blue, red opposite orange, 
+% and green opposite yellow), was created using  \verb!\SolvedConfig{R}{O}{W}{B}{G}{Y}!
+% (for the code see \ref{sec:codesolvedconfig}).
+%
+%
+%       \subsection{RubikCubeGrey command}
+%       \label{sec:rubikcubegrey}
+%
+%  \DescribeMacro{\RubikCubeGrey}
+%  \DescribeMacro{\RubikCubeGreyAll}
+%  The command \cmd{\RubikCubeGrey} generates a 3x3x3 cube with no colours allocated 
+%  \textit{except} for the central  cubie of each face, which takes the same colour 
+%  configuration as defined for the  \cmd{\RubikCubeSolved} command. 
+%  The command \cmd{\RubikCubeGreyAll} generates a cube with \textit{all} the faces 
+%  completely grey.
+%  Both these commands will accept either `grey' or  `gray' (to be consistent with TikZ).
+%
+%  These two commands, are designed to be  useful starting points when wanting to 
+%  describe the movement of particular cubies. We can see  the effect of 
+%  the \cmd{\RubikCubeGrey} command by viewing the cube in a semi-flat (SF) format, 
+%  as follows:
+%
+% \bigskip
+%
+% \RubikCubeGrey
+% \ShowCube{4.5cm}{0.45}{\DrawRubikCubeSF}
+%    \hspace{3mm}
+% \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+% \RubikCubeGrey
+% \ShowCube{4.5cm}{0.45}{\DrawRubikCubeSF}
+%\end{verbatim}
+% \end{minipage}
+%
+% \bigskip
+%  Users can easily set their own alternative  face/colour configuration either by `renewing' 
+% the \cmd{\RubikCubeGrey} command along the lines shown above (the code is 
+% in Section~\ref{sec:codegrey}), or simply creating a new `variant'  command 
+% altogether. 
+%
+%
+%
+%    \subsection{RubikSlice commands}
+%   \label{sec:slicecommands}
+%
+%  \DescribeMacro{\RubikSliceTopX}
+%  \DescribeMacro{\RubikSliceMiddleX}
+%  \DescribeMacro{\RubikSliceBottomX}
+%  These three commands  allocate the six visible cubie colours associated with  a
+%   \textit{horizontal}  slice of a Rubik cube. 
+% There are three pairs of  Slice commands; one pair 
+% (Left view \& Right view) for each of the horizontal  slices Top, Middle, Bottom.
+% The six colour arguments  associated with a given slice run in sequence 
+% from left to right irrespective of the viewpoint, e.g.,~\#1 \#2 \#3   \#4 \#5 \#6.
 %
-% The default width of the semi-flat cube representation is 10cm ($=3+3+1+3$), 
-% and that of the  flat cube is 12cm ($=3+3+3+3$). If in doubt check the extent of 
-% any horizontal white-space  using an fbox, or the \cmd{\ShowCubeF} command.
+% Since the viewpoint of the Rubik cube (from the Right or from the Left) 
+% influences which face the colours are associated with, it is necessary 
+% to have the view (R or L) specified in the command name.
 %
+% The format of the `slice' command is shown in the following example.
+% The Rubik  cube is shown from  the LeftDown (LD) view 
+% and consequently  each of the `slice' commands in this
+% particular example  ends in L, consistent with 
+% the final \cmd{\DrawRubikCubeLD} command.
+%
+% Note that the two legacy `Equator' versions (now replaced by `Middle') 
+% are retained to allow backward compatibility. 
+%
+% \bigskip
+%
+% \begin{minipage}{2.8cm}
+% \centering
+% \RubikFaceDownAll{Y}
+% \RubikSliceTopL    {G}{G}{G} {R}{R}{R}
+% \RubikSliceMiddleL {R}{R}{R} {B}{B}{B}
+% \RubikSliceBottomL {O}{O}{O} {G}{G}{G}
+% \begin{tikzpicture}[scale=0.7]
+% \DrawRubikCubeLD
+% \end{tikzpicture}%
+% \end{minipage}
+%    \hspace{5mm}
+% \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+%    \RubikFaceDownAll{Y}
+%    \RubikSliceTopL     {G}{G}{G} {R}{R}{R}
+%    \RubikSliceMiddleL  {R}{R}{R} {B}{B}{B}
+%    \RubikSliceBottomL  {O}{O}{O} {G}{G}{G}
+%    \ShowCube{3cm}{0.7}{\DrawRubikCubeLD}
+%\end{verbatim}
+% \end{minipage}
+%
+%
+%
+% \subsection{RubikSide commands}
+% \label{sec:rubikside}
+%
+%  \DescribeMacro{\RubikSideLeft} 
+%  \DescribeMacro{\RubikSideRight} 
+%  \DescribeMacro{\RubikSideFront}  
+%  \DescribeMacro{\RubikSideBack}  
+%  These RubikSide commands allocate colours to the side facelets of 
+%  the UP~face, and each  takes three ordered colour arguments, running from 
+%  top-left to top-right when looking directly at the side faces---see Section~\ref{sec:rubiksidecode}.
+%  These facelets are the top three facelets of each side Front, Back, Left, Right.
+%
+%  {\noindent}\textsc{usage}: \verb!\RubikSideBack{B}{G}{G}!
+%
+% \medskip
+%
+%   \DescribeMacro{\RubikSideLeftAll} 
+%   \DescribeMacro{\RubikSideRightAll} 
+%   \DescribeMacro{\RubikSideFrontAll}  
+%   \DescribeMacro{\RubikSideBackAll}
+%  These commands allocate the same colour to all three side cubies, and hence 
+%  take only a single colour argument.
+%
+%  {\noindent}\textsc{usage}: \verb!\RubikSideBackAll{R}!
+%
+% \medskip
+%
+%  The \cmd{\RubikSide..} and \cmd{\RubikFace..} commands are useful for setting up the colours  
+% for just part of the cube.  For~example, the following commands set-up the UP-face and sides, 
+% and then  draws the face and sidebars using \verb!\DrawFlatUpSide!.
+%
+%  \bigskip
+%  
+%  \begin{minipage}{4cm}
+%  \centering
+%\RubikFaceUp     {R}{Y}{R}%
+%                 {Y}{Y}{Y}%
+%                 {G}{Y}{B}%
+%\RubikSideBack{B}{G}{G}%
+%\RubikSideFront{Y}{R}{Y}%
+%\RubikSideRight{O}{B}{Y}%
+%\RubikSideLeft{Y}{O}{O}%
+%\ShowCube{2cm}{0.5}{\DrawFlatUpSide}
+%  \end{minipage}
+%        \hspace{1cm}
+%  \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+%%set up the UP face
+%\RubikFaceUp     {R}{Y}{R}%
+%                 {Y}{Y}{Y}%
+%                 {G}{Y}{B}%
+%\RubikSideBack{B}{G}{G}%
+%\RubikSideFront{Y}{R}{Y}%
+%\RubikSideRight{O}{B}{Y}%
+%\RubikSideLeft{Y}{O}{O}%
+%%draw the UP face and sides
+%\ShowCube{2cm}{0.5}{\DrawFlatUpSide}
+%\end{verbatim}
+%  \end{minipage}
+%
+% \bigskip
+%
+% Note that we could instead have drawn the above image using  \cmd{\DrawRubikLayer..}
+% commands. However, using the \cmd{\RubikSide..} and \cmd{\RubikFace..} commands
+% makes for a much more flexible and dynamic system, since the colours allocated using 
+% these  commands (provided they are external to  an environment)  will be global, 
+% and hence will follow subsequent  \cmd{\RubikRotation} commands.   
+%
+%
+%
+% \pagebreak
 %
 %
 %      \section{Rotation commands}
 %      \label{sec:RubikCommands} 
 %
-% We  use the standard Rubik cube notation  of WCA~(2012)---see article~12---and
-% also the `s' (Slice) and `a' (anti-Slice) notation described in   the 
-% `Notation and terminology' section
-% in the `Pretty patterns' page on the website of  
-% Fridrich (see References).
-% 
-% It is recommended  that  commas  are used to separate sequential 
-% Rubik moves or commands to avoid  ambiguity, especially when using just
-%  lettercodes on their own. 
-% For example, in the following sequence the commas  remove any ambiguity:
-%  \rr{U},\rr{Lw}2,\rr{Usp},\rr{Da} \ \ (|\rr{U},\rr{Lw}2,\rr{Usp},\rr{Da}|).
+% The Rubik bundle implements not only the standard Rubik cube notation  of the 
+% World Cube Association (see WCA website), but also the main variant notations 
+% used by the  Rubik interest groups and websites.  
+%
+% \begin{figure}[hbt]
+%  \centering
+%  \ifpdf
+%    \includegraphics[height=5cm]{rubik-doc-figA.pdf}
+%  \fi
+% \caption{\label{fig:notation}Face rotations} 
+% \end{figure}
+%
+% To avoid confusion the Rubik bundle uses a trailing `p' (lower-case) in rotation-codes to denote 
+% a `prime' (reversed direction); we also recommend that  commas  are used to separate 
+% sequential Rubik rotations (moves). 
+% While these are mainly to avoid  ambiguity,  they also greatly facilitate computer 
+% searching  and  copy-and-pasting  of rotation sequences.
+%
+%  Unfortunately, obtaining a good balance between an intuitive notation for defining
+%  rotations and the need for flexibility is difficult,
+% and consequently some notation is more intuitive than others. A good compromise 
+% seems to be the World Cube Association's FADN structure; i.e.,~Face (L,R,U,D,F,B), 
+% Action (m,w,s,a,c), Direction (p), 
+% N (n); for example, codes like \texttt{R, R2, Rc, Rm, Rwp, Rwp2} etc.  
+%
+%
+% The \rubikcube\  package  includes  commands for typesetting a wide range of 
+% rotation-codes (e.g.,~\rr{R}, \rr{y}, \rr{Bw}) and 
+% equivalent  hieroglyphs  (e.g.,~\rrh{R}, \rrh{y}, \rrh{Bw}), as well as commands
+% for typesetting  3x3x3 cubes and single cubies. All the rotation-codes and 
+% hieroglyphs are typeset using  one particular font \& size which we call the `rubikfont'
+% for convenience (see Section~\ref{sec:rubikfont} for details).
+% All of the rotation-codes described
+% here are recognised by the \textsc{rubikrotation} package 
+% (see Section~\ref{sec:rubikrotation}).
+%
+% Note that there are some rotation codes which  are not represented by arrow 
+% hieroglyphs, since their rotation  is not visible from the \textsc{front} face, 
+% and hence cannot easily be rendered as  an arrow hieroglyph. Consequently these 
+% rotations  have a simple `letter' hieroglyph 
+% in the form of the rotation-code in a square; for~example, \rrhBw, \rrhFm. 
 %
-% 
+%
+%  \pagebreak
 %
 %   \subsection{Overview}
 %     \label{sec:overview}
 %
-% The \rubikcube\  notation  comprises  a range of 
-% commands for moves or rotations (e.g.,~\rr{R}, \rr{y}, \rr{Bw}) and their equivalent  hieroglyphs 
-% (e.g.,~\rrh{R}, \rrh{y}, \rrh{Bw}), as well as commands for  drawing 3x3x3 cubes and single cubies.
-%
-% Note that there are a few rotation commands which  do not have arrow 
-% hieroglyphs---their their rotation  is not visible from the \textsc{front} face 
-% and hence cannot easily be rendered as  an arrow hieroglyph. Consequently these 
-% rotations  have a simple `letter' hieroglyph 
-% in the form of the rotation-code in a square; for example \rrhBw, \rrhSb. 
+% We now describe the four commands used for typesetting the various rotation-codes. 
 %
 % \DescribeMacro{\rr}
-%  The rotation-code of a rotation is typeset  (as in text) using the rubik-rotation 
-%  \cmd{\rr\marg{rotation-code}} command: i.e.,~\rr{R}\ is typeset using the command \cmd{\rr\{R\}}. 
-% The hieroglyph of a rotation command is generated  (in text) by
-% \DescribeMacro{\rrh}
-% using instead the command \cmd{\rrh\marg{rotation-code}}. Thus the command \cmd{\rrh\{R\}} generates 
-% \rrh{R}\  which is the hieroglyph associated with \rr{R}.
+%  The text version of a  rotation-code  is typeset  using the rubik-rotation 
+%  command \cmd{\rr\marg{rotation-code}}, i.e.,~\rr{R}\ is typeset using the command \cmd{\rr\{R\}}. 
+% The hieroglyph of a rotation is generated  (in text) by  \DescribeMacro{\rrh}
+% using instead the command \cmd{\rrh\marg{rotation-code}}. For~example, the command 
+% \cmd{\rrh\{R\}} generates  \rrh{R}\  which is the hieroglyph associated with
+% the rotation  \rr{R}.
 %
 % \DescribeMacro{\Rubik}
 % A vertically combined rotation-code  and its hieroglyph  is generated using the command 
-% \cmd{\Rubik\marg{rotation-code}}. For example, \Rubik{R}\ is generated by the command \cmd{\Rubik\{R\}}, 
+% \cmd{\Rubik\marg{rotation-code}}. For~example, \Rubik{R}\ is generated by the command \cmd{\Rubik\{R\}}, 
 % with  the square hieroglyph sitting on the baseline.
-% For some hieroglyphs (e.g.,~\rrh{x}, \rrh{y}, \rrh{z}\ denoting 90~degree axis rotations) 
-% the only  difference between the \cmd{\rrh\{\}} and \cmd{\Rubik\{\}} forms is that 
+% For some hieroglyphs (e.g.,~\rrh{x}, \rrh{y}, \rrh{z}\ denoting 90~degree cube-axis rotations) 
+% the only  difference between the \cmd{\rrh\{\}} and \cmd{\Rubik\{\}} form is that 
 % the \cmd{\Rubik\{\}}  form is elevated  to sit on the baseline just like the other
 %  \cmd{\Rubik\{\}} hieroglyphs. 
-% For example \cmd{\rrh\{yp\}} generates \rrh{yp}, while
+% For~example, \cmd{\rrh\{yp\}} generates \rrh{yp}, while
 % \cmd{\Rubik\{yp\}} generates \Rubik{yp}.
 % 
 % \DescribeMacro{\textRubik}
 % A horizontally combined  rotation-code and its hieroglyph (in sequence as in text) 
-% is generated using  the command stem  \cmd{\textRubik\marg{rotation-code}}. 
-% For example,  \textRubik{R}\ is typeset using the command \cmd{\textRubik\{R\}}.
-% A list of all commands and their associated  hieroglyphs is given in
+% is generated using  the command   \cmd{\textRubik\marg{rotation-code}}. 
+% For~example,  \textRubik{R}\ is typeset using the command \cmd{\textRubik\{R\}}.
+% A list of all rotation-code commands and their associated  hieroglyphs is given in
 %  Section~\ref{sec:listofcommands}. 
 %
-% \pagebreak
+%
 %
 % \subsection{Face rotations}
 %
@@ -688,10 +1270,10 @@
 % \DescribeMacro{B}
 % The six main faces of the cube are denoted as \textsc{front} (towards the observer), 
 % \textsc{back},  \textsc{left}, \textsc{right},  \textsc{up}, \textsc{down}.
-% The uppercase initial letter  of each face-name (\rr{F}, \rr{B}, \rr{L}, \rr{R}, \rr{U}, \rr{D}) 
+% The upper-case initial letter  of each face-name (\rr{F}, \rr{B}, \rr{L}, \rr{R}, \rr{U}, \rr{D}) 
 % denotes a clockwise 90-degree rotation of the  face as shown in  
 % Figure~\ref{fig:notation}. 
-% For example, \rr{D}\ is generated by the `rubik rotation' command \cmd{\rr\{D\}}.
+% For~example, \rr{D}\ is generated by the `rubik rotation' command \cmd{\rr\{D\}}.
 %
 % \DescribeMacro{Up}
 % \DescribeMacro{Dp}
@@ -701,57 +1283,69 @@
 % \DescribeMacro{Bp}
 %  An appended  prime~$^\prime$ indicates an anticlockwise rotation; e.g.,~\rr{Fp}. 
 %  This is sometimes written as  \rr{F}$\boldmath{^{-1}}$. The `prime' notation is 
-%  achieved by appending a lowercase `p' to the face rotation command. For example, \rr{Rp}\ 
-%  is generated by \cmd{\rr\{Rp\}}. 
+%  achieved by appending a lower-case `p' to the face rotation command. For~example, \rr{Rp}\ 
+%  is generated by \cmd{\rr\{Rp\}}. More formally, \rr{Rp} is the `inverse' of  \rr{R}.
 %
-% \vspace{-0.2cm}
-% \begin{figure}[hbt]
-%  \centering
-%  \ifpdf
-%    \includegraphics[height=5cm]{Rubik-doc-figA.pdf}
-%  \fi
-% \caption{\label{fig:notation}} 
-% \end{figure}
+%  The superscript~$^2$, or sometimes just an ordinary~2, indicates that the rotation
+%  is applied twice. For~example, \rr{R}\textbf{$^2$} or \rr{R}\textbf{2} 
+%  denote  \textit{two} successive 90~degree clockwise rotations of the \textsc{right} face;
+%   \rr{R}\textbf{$^3$} is equivalent to \rr{Rp} etc. 
 %
 %
-%      \subsection{Slice rotations}
+%      \subsection{Inner-slice rotations}
 %      \label{sec:slicerotations}
 %
-% \DescribeMacro{Su}
-% \DescribeMacro{Sd}
-% \DescribeMacro{Sl}
-% \DescribeMacro{Sr}
-% \DescribeMacro{Sf}
-% \DescribeMacro{Sb}
-% The Rubik cube (3x3x3) has three orthogonal so-called `inner' slices, whose +ve 
-% rotation  direction follows that of a named face. For example the inner slice 
+% The Rubik cube (3x3x3) has three orthogonal so-called 
+% `inner' slices (middle layers, middle slices), whose +ve 
+% rotation  direction follows that of a named face. For~example, the inner-slice 
 % rotation  between the \textsc{right} and \textsc{left} faces  whose rotation 
-% direction follows the rotation \rr{R}\ (rotation is isomorphic to \rr{R}) is denoted 
-% as \rr{Sr}, which is typeset using the command \cmd{\rr\{Sr\}}. Note that in these cases
-%  the trailing  \texttt{r}  in the command  is lowercase.
-%
-% \bigskip\bigskip\bigskip
-%
-% \DescribeMacro{Sup}
-% \DescribeMacro{Sdp}
-% \DescribeMacro{Slp}
-% \DescribeMacro{Srp}
-% \DescribeMacro{Sfp}
-% \DescribeMacro{Sbp}
-% Each of these slice rotations (S rotations) has a reversed (primed)  p-form,
-% the command for which is generated by appending the suffix `p'.
-% For example  the inner slice rotations  \rr{Slp}\ (\cmd{\rr\{Slp\}}) and 
-% \rr{Sr}\ (\cmd{\rr\{Sr\}}) are identical.
-% The equivalence is more obvious when we see their respective hieroglyphs.
-% For example, in this case \linebreak \rr{Slp}\ (\cmd{\rr\{Slp\}}) 
-%  $\equiv$ \rrh{Slp}\ (\cmd{\rrh\{Slp\}}), 
-%  and  \rr{Sr}\ (\cmd{\rr\{Sr\}}) $\equiv$ \rrh{Sr}\ (\cmd{\rrh\{Sr\}}). 
-%
-% \bigskip
-%
-% \pagebreak
-%
-%        \subsubsection*{MES slice notation}
+% direction follows the rotation \rr{R}\ (i.e.,~its rotation is isomorphic to \rr{R}).
+%  The  inner-slice rotations form a group (the Slice group), originally 
+% described by John Conway (Frey and Singmaster, 1982, p~105).
+%
+%
+% \subsubsection*{The `m' notation}
+%  \label{sec:mnotation}
+%
+% \DescribeMacro{Um}
+% \DescribeMacro{Dm}
+% \DescribeMacro{Lm}
+% \DescribeMacro{Rm}
+% \DescribeMacro{Fm}
+% \DescribeMacro{Bm}
+% Here `m' stands for the `middle' slice, namely  that parallel to the  designated 
+% \textsc{face}; its rotation mirrors that of the 
+% \textsc{face}.   The \texttt{m}  must be in lower-case. 
+% Each of these  rotation-codes has a complementary `prime' version, formed 
+% by appending a `p'; for~example,  \rr{Rm}  (\verb!\rr{Rm}!) is a middle layer rotation 
+% \rrh{Rm} between the  \textsc{right} and \textsc{left} faces, and is in the same
+% direction as \rr{R}. The code \rr{Rmp} (\verb!\rr{Rmp}!) refers to the same 
+% middle slice, but rotated in  the opposite direction \rrh{Rmp}.
+%
+%  This notation, which was probably  invented by Singmaster, was originally used on the 
+%  Cube Lovers usenet group (1981--1997). It is now much used on the 
+%  Jaap Puzzles website (see Scherphius J) ---see also Section~\ref{sec:codeJaap}.
+%
+%
+% \subsubsection*{The `M' notation} 
+%  \label{sec:Mnotation}
+%
+% \DescribeMacro{MU}
+% \DescribeMacro{MD}
+% \DescribeMacro{ML}
+% \DescribeMacro{MR}
+% \DescribeMacro{MF}
+% \DescribeMacro{MB}
+% This variant of the above  `middle' slice notation (e.g.,~\texttt{MR} $\equiv$ \texttt{Rm}) 
+% is part of the  `superset' notation of  Randelshofer. As before,  the rotation  
+% direction follows that  of the designated   \textsc{face}. 
+% Each has a complementary  `prime' version  
+% formed by appending a `p'.   The \texttt{M}  must be in upper-case.
+%
+%
+% \bigskip\bigskip
+%
+% \subsubsection*{The MES notation}
 %
 % \DescribeMacro{M}
 % \DescribeMacro{E}
@@ -759,8 +1353,8 @@
 % \DescribeMacro{Mp}
 % \DescribeMacro{Ep}
 % \DescribeMacro{Sp}
-% An alternative and somewhat confusing (and hence is non-standard) slice notation
-%  which is sometimes used  is the following 
+% An alternative but very confusing 
+% inner-slice notation (e.g.,~\texttt{Ep} $\equiv$ \texttt{Um}) which is occasionally used  is the 
 % so-called MES notation,  as used in the Waterman algorithm
 %  (Treep and Waterman 1987).
 % \begin{itemize}
@@ -771,16 +1365,28 @@
 %  \item[\rr{S}] \  (\textsc{standing} \rrh{S}, between the \textsc{front} and 
 %      \textsc{back} faces;   direction follows \rr{F}).
 % \end{itemize}
-% Each of these also has a reversed (prime) version, and  a hieroglyph 
-% (see Section~\ref{sec:listofcommands}).
-% The equivalent S notation (see above) is therefore 
-% as follows:  \rr{E}\ $\equiv$ \rr{Sd},  \rr{Ep}\ $\equiv$ \rr{Su}, 
-% \rr{M}\ $\equiv$ \rr{Sl}, \rr{Mp}\ $\equiv$ \rr{Sr}, \rr{S}\ $\equiv$ \rr{Sf}, 
-%  \rr{Sp}\ $\equiv$ \rr{Sb}. 
+% Each of these also has an inverse (prime) version.
+%
+%
+% \subsubsection*{The `S' notation}
+%
+% \DescribeMacro{Su}
+% \DescribeMacro{Sd}
+% \DescribeMacro{Sl}
+% \DescribeMacro{Sr}
+% \DescribeMacro{Sf}
+% \DescribeMacro{Sb}
+% In this equally confusing inner-slice notation, `S' stands for `inner-slice'; 
+% the face letter must  be in lower-case (e.g.,~\texttt{Sr} $\equiv$ \texttt{Rm}). For~example, the inner-slice 
+% rotation  between the \textsc{right} and \textsc{left} faces  whose rotation 
+% direction follows the rotation \rr{R}\ is denoted 
+% as \rr{Sr}, which is typeset using the command \cmd{\rr\{Sr\}}. 
+% Each has an inverse  (prime)  p-form.
 %
-% 
 %
-% \subsubsection*{Singmaster slice notation}
+%     \subsection{Outer-slice rotations}
+%
+% \subsubsection*{Slice notation}
 %
 % \DescribeMacro{Us}
 % \DescribeMacro{Ds}
@@ -788,20 +1394,38 @@
 % \DescribeMacro{Rs}
 % \DescribeMacro{Fs}
 % \DescribeMacro{Bs}
-% These are an alternative (but somewhat less intuitive) form of  
-% slice notation  which can be thought of as complementing the 
-% inner slice  rotations. These were originally described by 
-% Singmaster (Frey and Singmaster, 1982).
-% See the link to `notation' on the `Pretty patterns' page of the 
-% Fridrich website.
+% This is a  `paired' form of  
+% notation (two rotations at once), which can be thought of as complementing the 
+% inner-slice  (middle layer) rotations. 
+% Each of these `slice' commands denotes a  rotation of  two opposite faces 
+% in the \textit{same}  direction.
+% {\linebreak}For~example, \textRubik{Us}\ $\equiv$ \textRubik{U}\ + \textRubik{Dp};
+% i.e.,~both face-rotations are in the \textit{same} direction 
+% as \rr{U}. Each of these rotation-codes has a complementary `anti-slice' version (see below).
 %
-% Each of these commands denotes a  rotation of  two opposite faces 
-% in the same  direction. For example, \textRubik{Us}\ $\equiv$ \textRubik{U}\ + \textRubik{Dp}, 
-% which is typeset as: 
-% \newline |\textRubik{Us}\ $\equiv$ \textRubik{U}\ + \textRubik{Dp}|, 
-% i.e.,~for  \rr{Us}\ both face-rotations are in the \textit{same} direction 
-% as \rr{U}. 
+% This notation was originally described by 
+% Singmaster (Frey and Singmaster, 1982), and is much used 
+% on the `Pretty patterns' page of the Fridrich website (this 
+% page also has a useful link to `notation').
+%
+%
+% \bigskip
 %
+% \DescribeMacro{SU}
+% \DescribeMacro{SD}
+% \DescribeMacro{SL}
+% \DescribeMacro{SR}
+% \DescribeMacro{SF}
+% \DescribeMacro{SB}
+% This variant of the above `slice'  notation (e.g.,~\texttt{SU} $\equiv$ \texttt{Us})
+%  is part of the  `superset'  notation of Randelshofer. As before,  the rotation  
+% direction follows that of the designated 
+%  \textsc{face}. Each has a complementary  `prime' version  formed by appending a `p'. 
+% 
+%
+% \bigskip\bigskip 
+%
+
 %
 % \subsubsection*{Anti-slice notation}
 %
@@ -813,11 +1437,9 @@
 % \DescribeMacro{Ba}
 % Each of these commands denotes a  rotation of  two opposite faces 
 % in \textit{opposite}  directions. 
-% For example, \textRubik{Ua}\ $\equiv$ \textRubik{U}\ + \textRubik{D}, 
-% which is typeset as: 
-% \newline |\textRubik{Ua}\ $\equiv$ \textRubik{U}\ + \textRubik{D}|.
-% See the link to `notation' on the `Pretty patterns' page of the 
-% Fridrich website.
+% For~example, \textRubik{Ua}\ $\equiv$ \textRubik{U}\ + \textRubik{D}.
+% This notation is much used  on the `Pretty patterns' page of the 
+% Fridrich website (see the note above re: `slice notation').
 %
 %   \bigskip\bigskip
 %
@@ -829,19 +1451,32 @@
 % \DescribeMacro{Rw}
 % \DescribeMacro{Fw}
 % \DescribeMacro{Bw}
-% The  clockwise \textit{combined} rotation of  an outer face AND its inner slice 
-% (officially known as a `double outer slice' rotation) is denoted by appending a 
-% lowercase  \textbf{\textsf{\footnotesize{w}}} (denoting `wide') to a face rotation command.
-% For example,  a \textsc{right} double outer slice rotation is  denoted as \rr{Rw}. 
-% Similarly, the prime $^\prime$ version \rr{Lwp}\  is generated by \cmd{\rr\{Lwp\}}.
+% The  clockwise \textit{combined} rotation of  an outer face AND its inner-slice 
+% (officially known as a `double outer slice' rotation, or a `double block' move) 
+% is denoted by appending a  lower-case  \textbf{\textsf{\footnotesize{w}}} 
+% (denoting `wide') to a rotation-code (endorsed  by the WCA).
+% For~example,  a \textsc{right} double outer slice rotation \rrh{Rw} (\verb!\rrh{Rw}!) 
+% is  denoted as \rr{Rw} (\verb!\rr{Rw}!).  The `prime' version is formed by 
+% appending a `p' to the rotation-code. For~example,  \rr{Rwp}\  is generated by \verb!\rr{Rwp}!.
 %
-%  The superscript~$^2$, or sometimes just an ordinary 2, indicates that the rotation
-%  is applied twice. For example \rr{R}\textbf{$^2$} or \rr{R}\textbf{2} 
-%  denote  \textit{two} successive 90~degree clockwise rotations of the \textsc{right} face.
-% Clearly \rr{R}\textbf{$^3$} is equivalent to \rr{Rp} etc.
 %
+% \bigskip
 %
+% \subsubsection*{The `T' notation} 
+%  \label{sec:Tnotation}
 %
+% \DescribeMacro{TU}
+% \DescribeMacro{TD}
+% \DescribeMacro{TL}
+% \DescribeMacro{TR}
+% \DescribeMacro{TF}
+% \DescribeMacro{TB}
+% This confusing variant of the above `w' notation (e.g.,~\texttt{TR} $\equiv$ \texttt{Rw}) is part of 
+% the  `superset'  notation of Randelshofer. As before,  the rotation  direction 
+% follows that of the designated \textsc{face}. Each has a complementary `prime' version  
+% formed by appending a `p'. 
+%
+%   \bigskip\bigskip
 %
 %     \subsection{Axis rotations}
 %
@@ -854,17 +1489,17 @@
 % with their hieroglyphs (the \cmd{\rrh\{\}} forms) being denoted 
 % as \rrh{x}, \rrh{y}, \rrh{z}\ in order to distinguish them from  square layer-rotation 
 % hieroglyphs.
-% Note that since \rr{x}, \rr{y}, \rr{z}\ rotations are always expressed in lowercase, 
-%  this practice is extended also to the commands. 
+% Note that since \rr{x}, \rr{y}, \rr{z}\ rotations are always expressed in lower-case;
+%  this practice is also extended  to the commands. 
 %
-% An \rr{x}\textbf{2} rotation (two \rr{x}\ rotations one after 
+% For example, an \rr{x}\textbf{2} rotation (two \rr{x}\ rotations one after 
 % the other, i.e.,~\rrh{x}\ \rrh{x}) denotes rotating 
 % the cube 180~degrees about its x axis so as to bring the \textsc{down} face  
 % into the \textsc{up} position.
 %
 %  An appended  prime~$^\prime$ indicates an anticlockwise rotation; 
-% for example, \rr{xp}\ (which is generated by appending a `p' to the end of 
-% the command, i.e.,~\cmd{\rr\{xp\}}). 
+% for~example, \rr{xp}\ (which is generated by appending a `p' to the  
+% rotation-code, i.e.,~\cmd{\rr\{xp\}}). 
 %
 % The \cmd{\Rubik\{\}}  forms (and their prime `p' versions) generate the same
 %  hieroglyphs  as their \cmd{\rrh\{\}} versions, except that their spacing is 
@@ -886,7 +1521,7 @@
 % \DescribeMacro{b}
 % A commonly used  alternative for the \rr{x}, \rr{y}, \rr{z}\ notation 
 % (and endorsed  by the WCA)  uses these 
-% lowercase face letter to denote a 90~degree whole-cube rotation  in the same 
+% lower-case face letter to denote a 90~degree whole-cube rotation  in the same 
 % directional sense as that of the   standard face rotations. 
 %
 % {\noindent}Thus  
@@ -894,24 +1529,62 @@
 % \rr{l}\ $\equiv$ \rr{xp}, \   \rr{r}\ $\equiv$ \rr{x}, \ 
 % \rr{f}\ $\equiv$ \rr{z}, \    \rr{b}\ $\equiv$ \rr{zp},
 %
-% {\noindent}For example, \rr{d}\ is generated by  the command \cmd{\rr\{d\}}.
+% {\noindent}For~example, \rr{d}\ is generated by  the command \cmd{\rr\{d\}}.
 %
 % {\noindent}Note that these rotations do not have prime $^\prime$ versions  
 % since \rr{u}~is the opposite of \rr{d}, \rr{l}~is the opposite of \rr{r}, and
 % \rr{f}~is the opposite of \rr{b}.
 %
-% As with the \rrh{x}, \rrh{y}, \rrh{z}\ forms (described above) there also 
-% equivalent \cmd{\rrh\{\}} and \cmd{\Rubik\{\}} forms. For example, 
+% As with the \rrh{x}, \rrh{y}, \rrh{z}\ forms (described above) there are also 
+% equivalent \cmd{\rrh\{\}} and \cmd{\Rubik\{\}} forms. For~example, 
 % \rrh{d}\ is generated by the command \cmd{\rrh\{d\}}.
 %
 %
+% \subsubsection*{The `c' notation} 
+%  \label{sec:cnotation}
+%
+% \DescribeMacro{Uc}
+% \DescribeMacro{Dc}
+% \DescribeMacro{Lc}
+% \DescribeMacro{Rc}
+% \DescribeMacro{Fc}
+% \DescribeMacro{Bc}
+% This slightly more intuitive notation (the `c' stands for `cube') also associates the rotation 
+% direction  with that of the designated  \textsc{face} (e.g.,~\texttt{Rc} $\equiv$ \texttt{x}).
+%  Each has a complementary `prime' version  formed by appending a `p'.  
+% For~example, \rr{Rc} (\verb!\rr{Rc}!) is equivalent to \rr{x}; 
+%  \rr{Rcp} (\verb!\rr{Rcp}!) is equivalent to \rr{xp}.  
+%
+%  This notation, which was probably invented by Singmaster, was originally used on the 
+%  Cube Lovers usenet group (1981--1997). It is now much used on the 
+%  Jaap Puzzles website (see Scherphius J) ---see also Section~\ref{sec:codeJaap}.
+%
+% \bigskip\bigskip
+%
+% \subsubsection*{The `C' notation} 
+%  \label{sec:Cnotation}
+%
+% \DescribeMacro{CU}
+% \DescribeMacro{CD}
+% \DescribeMacro{CL}
+% \DescribeMacro{CR}
+% \DescribeMacro{CF}
+% \DescribeMacro{CB}
+% This variant of the whole cube rotation notation 
+% (e.g.,~\texttt{CR} $\equiv$ \texttt{Rc} $\equiv$ \texttt{x}) 
+% is part of the  `superset' notation of Randelshofer. As before, the rotation  
+% direction follows that of the designated  \textsc{face}. Each has a complementary 
+% `prime' version  formed by appending a `p'. 
+%
+%
+% \bigskip% \bigskip
 %
 %  \subsection{Examples}
 %  \label{sec:examples}
 %  
-%    {\noindent}\rr{R}\  is generated by  the `rubik rotation' command \cmd{\rr\{R\}}
+%    {\noindent}\rr{R}\  is generated by  the  command \cmd{\rr\{R\}}
 %
-%    {\noindent}\rr{Fw}\  is generated by  the `rubik rotation' command \cmd{\rr\{Fw\}}
+%    {\noindent}\rr{Fw}\  is generated by  the  command \cmd{\rr\{Fw\}}
 %
 %    {\noindent}\rr{L}$^2$ is generated by \cmd{\rr\{L\}}\verb!$^2$!
 %
@@ -924,7 +1597,7 @@
 %    {\noindent}\rr{x}\ and \rrh{y}\ and \Rubik{zp}\ are  generated by 
 %   \cmd{\rr\{x\}}  and \cmd{\rrh\{y\}} and \cmd{\Rubik\{zp\}}
 %
-%    {\noindent}\rr{f}\ and \rrh{b}\ are  generated by \cmd{\rr\{f\}} and \cmd{\rrh\{b\}}
+%    {\noindent}\rr{Fc}\ and \rrh{Bc}\ are  generated by \cmd{\rr\{Fc\}} and \cmd{\rrh\{Bc\}}
 %
 %   {\noindent}\rr{U}\rr{U}\rr{R}\rr{R}\ is generated by
 %      \cmd{\rr\{U\}}\cmd{\rr\{U\}}\cmd{\rr\{R\}}\cmd{\rr\{R\}}
@@ -941,7 +1614,7 @@
 %  
 %  \bigskip
 % 
-% {\noindent}Commas can be important in avoiding  ambiguity; for example
+% {\noindent}Commas can be important in avoiding  ambiguity; for~example,
 %
 % \bigskip
 %
@@ -956,35 +1629,48 @@
 %  {\noindent}\rrh{F}\rrh{U}\rrh{y}\rrh{Rp}\rrh{Lwp} \ \ \ \
 %  \verb!\rrh{F}\rrh{U}\rrh{y}\rrh{Rp}\rrh{Lwp}! 
 %
+% \bigskip
+%
+% Note that if each rotation element uses the \textit{same} font or encoding, then 
+% typesetting a rotation  sequence  can be achieved more easily using the 
+% \verb!\ShowSequence! command (see Section~\ref{sec:showsequence}). For example, we can  
+% typeset the last sequence much more conveniently, as follows:
+%
+% \medskip
+%
+% \verb!\ShowSequence{}{\rrh}{F,U,y,Rp,Lwp}! \ \ $\rightarrow$ \ \ \ShowSequence{}{\rrh}{F,U,y,Rp,Lwp}
 %
 %
-%  \bigskip
 %
 %  \subsection{Backwards compatibility}
 %   \label{sec:backwardscompat}
 %
 % Note that in keeping with `backwards compatibility'  all rotation commands (see below) 
-% can still  be written without the usual curley braces \verb!{}!. 
-% For example,  the hieroglyph \rrhD\  (\cmd{\rrh\{D\}}) can also be generated using the command
+% can still  be written without the usual curly braces \verb!{}!. 
+% For~example,  the hieroglyph \rrhD\  (\cmd{\rrh\{D\}}) can also be generated using the command
 %   \cmd{\rrhD}. 
 %
 %  \bigskip
 %
+% \pagebreak
+%
 %  \subsection{Listing of all rotation commands}
 %   \label{sec:listofcommands}
 %
 %
 % Note that all the commands presented here also have a \cmd{\Rubik\{\}} equivalent form which 
 % typesets both the hieroglyph and its lettercode in a vertical format, 
-% as shown in the `Examples' section above. These have been ommitted  here
+% as shown in the `Examples' section above. These have been   omitted  here
 % owing to the difficulty of including this form easily in the following table.
 %
-% Note also that some \cmd{\rrh\{\}} commands (eg~the \cmd{\rrh\{B\}} command)  
+%
+% Note also that some \cmd{\rrh\{\}} commands (e.g.,~the \cmd{\rrh\{B\}} command)  
 % show only the lettercode in a square box, e.g.,~\rrh{B}. This is because these  rotations
 %  do not have a `true' visual representation as seen from the \textsc{front} face,
 % and hence can be somewhat ambiguous unless typeset with their associated 
 % lettercode. 
 %
+%
 %  \newcommand{\dnstrut}{\rule{0pt}{17pt}}
 %  \newcommand{\dns}{\hspace{2mm}}
 %  \newcommand{\dnsp}{\hspace{2mm}} 
@@ -1016,6 +1702,18 @@
 %  \dnstrut\rr{Uap}\dns\cmd{\rr\{Uap\}}
 %  & \rrh{Uap}\dns\cmd{\rrh\{Uap\}}
 %  & \textRubik{Uap}\dns\cmd{\textRubik\{Uap\}} \nonumber\\
+%   \dnstrut\rr{Um}\dns\cmd{\rr\{Um\}}
+%  & \rrh{Um}\dns\cmd{\rrh\{Um\}}
+%  & \textRubik{Um}\dns\cmd{\textRubik\{Um\}} \nonumber\\   
+%  \dnstrut\rr{Ump}\dns\cmd{\rr\{Ump\}}
+%  & \rrh{Ump}\dns\cmd{\rrh\{Ump\}}
+%  & \textRubik{Ump}\dns\cmd{\textRubik\{Ump\}} \nonumber\\
+%    \dnstrut\rr{Uc}\dns\cmd{\rr\{Uc\}}
+%  & \rrh{Uc}\dns\cmd{\rrh\{Uc\}}
+%  & \Rubik{Uc}\dns\cmd{\Rubik\{Uc\}} \nonumber\\   
+%  \dnstrut\rr{Ucp}\dns\cmd{\rr\{Ucp\}}
+%  & \rrh{Ucp}\dns\cmd{\rrh\{Ucp\}}
+%  & \Rubik{Ucp}\dns\cmd{\Rubik\{Ucp\}} \nonumber\\ 
 %  \end{supertabular}
 %
 %
@@ -1044,6 +1742,18 @@
 %  \dnstrut\rr{Dap}\dns\cmd{\rr\{Dap\}}
 %  & \rrh{Dap}\dns\cmd{\rrh\{Dap\}}
 %  & \textRubik{Dap}\dns\cmd{\textRubik\{Dap\}} \nonumber\\
+%    \dnstrut\rr{Dm}\dns\cmd{\rr\{Dm\}}
+%  & \rrh{Dm}\dns\cmd{\rrh\{Dm\}}
+%  & \textRubik{Dm}\dns\cmd{\textRubik\{Dm\}} \nonumber\\ 
+%  \dnstrut\rr{Dmp}\dns\cmd{\rr\{Dmp\}}
+%  & \rrh{Dmp}\dns\cmd{\rrh\{Dmp\}}
+%  & \textRubik{Dmp}\dns\cmd{\textRubik\{Dmp\}} \nonumber\\ 
+%  \dnstrut\rr{Dc}\dns\cmd{\rr\{Dc\}}
+%  & \rrh{Dc}\dns\cmd{\rrh\{Dc\}}
+%  & \Rubik{Dc}\dns\cmd{\Rubik\{Dc\}} \nonumber\\ 
+%  \dnstrut\rr{Dcp}\dns\cmd{\rr\{Dcp\}}
+%  & \rrh{Dcp}\dns\cmd{\rrh\{Dcp\}}
+%  & \Rubik{Dcp}\dns\cmd{\Rubik\{Dcp\}} \nonumber\\ 
 %  \end{supertabular}
 %
 %
@@ -1072,9 +1782,20 @@
 %  \dnstrut\rr{Lap}\dns\cmd{\rr\{Lap\}}
 %  & \rrh{Lap}\dns\cmd{\rrh\{Lap\}}
 %  & \textRubik{Lap}\dns\cmd{\textRubik\{Lap\}} \nonumber\\
+%  \dnstrut\rr{Lm}\dns\cmd{\rr\{Lm\}}
+%  & \rrh{Lm}\dns\cmd{\rrh\{Lm\}}
+%  & \textRubik{Lm}\dns\cmd{\textRubik\{Lm\}} \nonumber\\   
+%  \dnstrut\rr{Lmp}\dns\cmd{\rr\{Lmp\}}
+%  & \rrh{Lmp}\dns\cmd{\rrh\{Lmp\}}
+%  & \textRubik{Lmp}\dns\cmd{\textRubik\{Lmp\}} \nonumber\\ 
+%  \dnstrut\rr{Lc}\dns\cmd{\rr\{Lc\}}
+%  & \rrh{Lc}\dns\cmd{\rrh\{Lc\}}
+%  & \Rubik{Lc}\dns\cmd{\Rubik\{Lc\}} \nonumber\\ 
+%  \dnstrut\rr{Lcp}\dns\cmd{\rr\{Lcp\}}
+%  & \rrh{Lcp}\dns\cmd{\rrh\{Lcp\}}
+%  & \Rubik{Lcp}\dns\cmd{\Rubik\{Lcp\}} \nonumber\\ 
 %  \end{supertabular}
 %
-%
 %  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4.5cm}}
 %  \dnstrut\rr{R}\dns\cmd{\rr\{R\}}
 %  & \rrh{R}\dns\cmd{\rrh\{R\}}
@@ -1100,6 +1821,18 @@
 %  \dnstrut\rr{Rap}\dns\cmd{\rr\{Rap\}}
 %  & \rrh{Rap}\dns\cmd{\rrh\{Rap\}}
 %  & \textRubik{Rap}\dns\cmd{\textRubik\{Rap\}} \nonumber\\
+%  \dnstrut\rr{Rm}\dns\cmd{\rr\{Rm\}}
+%  & \rrh{Rm}\dns\cmd{\rrh\{Rm\}}
+%  & \textRubik{Rm}\dns\cmd{\textRubik\{Rm\}} \nonumber\\ 
+%  \dnstrut\rr{Rmp}\dns\cmd{\rr\{Rmp\}}
+%  & \rrh{Rmp}\dns\cmd{\rrh\{Rmp\}}
+%  & \textRubik{Rmp}\dns\cmd{\textRubik\{Rmp\}} \nonumber\\ 
+%  \dnstrut\rr{Rc}\dns\cmd{\rr\{Rc\}}
+%  & \rrh{Rc}\dns\cmd{\rrh\{Rc\}}
+%  & \Rubik{Rc}\dns\cmd{\Rubik\{Rc\}} \nonumber\\ 
+%  \dnstrut\rr{Rcp}\dns\cmd{\rr\{Rcp\}}
+%  & \rrh{Rcp}\dns\cmd{\rrh\{Rcp\}}
+%  & \Rubik{Rcp}\dns\cmd{\Rubik\{Rcp\}} \nonumber\\ 
 %  \end{supertabular}
 %
 %
@@ -1128,6 +1861,18 @@
 %  \dnstrut\rr{Fap}\dns\cmd{\rr\{Fap\}}
 %  & \rrh{Fap}\dns\cmd{\rrh\{Fap\}}
 %  & \textRubik{Fap}\dns\cmd{\textRubik\{Fap\}} \nonumber\\
+%  \dnstrut\rr{Fm}\dns\cmd{\rr\{Fm\}}
+%  & \rrh{Fm}\dns\cmd{\rrh\{Fm\}}
+%  & \textRubik{Fm}\dns\cmd{\textRubik\{Fm\}} \nonumber\\ 
+%  \dnstrut\rr{Fmp}\dns\cmd{\rr\{Fmp\}}
+%  & \rrh{Fmp}\dns\cmd{\rrh\{Fmp\}}
+%  & \textRubik{Fmp}\dns\cmd{\textRubik\{Fmp\}} \nonumber\\ 
+%  \dnstrut\rr{Fc}\dns\cmd{\rr\{Fc\}}
+%  & \rrh{Fc}\dns\cmd{\rrh\{Fc\}}
+%  & \Rubik{Fc}\dns\cmd{\Rubik\{Fc\}} \nonumber\\ 
+%  \dnstrut\rr{Fcp}\dns\cmd{\rr\{Fcp\}}
+%  & \rrh{Fcp}\dns\cmd{\rrh\{Fcp\}}
+%  & \Rubik{Fcp}\dns\cmd{\Rubik\{Fcp\}} \nonumber\\ 
 %  \end{supertabular}
 %
 %
@@ -1156,6 +1901,18 @@
 %  \dnstrut\rr{Bap}\dns\cmd{\rr\{Bap\}}
 %  & \rrh{Bap}\dns\cmd{\rrh\{Bap\}}
 %  & \textRubik{Bap}\dns\cmd{\textRubik\{Bap\}} \nonumber\\
+%  \dnstrut\rr{Bm}\dns\cmd{\rr\{Bm\}}
+%  & \rrh{Bm}\dns\cmd{\rrh\{Bm\}}
+%  & \textRubik{Bm}\dns\cmd{\textRubik\{Bm\}} \nonumber\\ 
+%  \dnstrut\rr{Bmp}\dns\cmd{\rr\{Bmp\}}
+%  & \rrh{Bmp}\dns\cmd{\rrh\{Bmp\}}
+%  & \textRubik{Bmp}\dns\cmd{\textRubik\{Bmp\}} \nonumber\\ 
+%  \dnstrut\rr{Bc}\dns\cmd{\rr\{Bc\}}
+%  & \rrh{Bc}\dns\cmd{\rrh\{Bc\}}
+%  & \Rubik{Bc}\dns\cmd{\Rubik\{Bc\}} \nonumber\\   
+%  \dnstrut\rr{Bcp}\dns\cmd{\rr\{Bcp\}}
+%  & \rrh{Bcp}\dns\cmd{\rrh\{Bcp\}}
+%  & \Rubik{Bcp}\dns\cmd{\Rubik\{Bcp\}} \nonumber\\ 
 %  \end{supertabular}
 %
 %
@@ -1265,43 +2022,171 @@
 %  \end{supertabular}
 %
 %
-% \pagebreak
+%    \subsubsection{Randelshofer notation}
+%     \label{sec:listofRandelshofercommands}
 %
-%       \section{Other commands}
+%  \newcommand{\dnRubik}[1]{%
+%    \dnstrut\rr{#1}\dns\cmd{\rr\{#1\}}%
+%    & \rrh{#1}\dns\cmd{\rrh\{#1\}}%
+%    & \Rubik{#1}\dns\cmd{\Rubik\{#1\}} \nonumber\\%
+%    }%  
 %
+%  \newcommand{\dntextRubik}[1]{%
+%   \dnstrut\rr{#1}\dns\cmd{\rr\{#1\}}%
+%   & \rrh{#1}\dns\cmd{\rrh\{#1\}}%
+%   & \textRubik{#1}\dns\cmd{\textRubik\{#1\}} \nonumber\\%
+%   }%
 %
-% \DescribeMacro{\rubikcube}
-% This command generates the logo \rubikcube.
 %
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4.5cm}}
+%   \dnRubik{CR}
+%   \dnRubik{CRp}
+%   \dnRubik{CL}
+%   \dnRubik{CLp}
+%   \dnRubik{CU}
+%   \dnRubik{CUp}
+%   \dnRubik{CD}
+%   \dnRubik{CDp}
+%   \dnRubik{CF}
+%   \dnRubik{CFp}
+%   \dnRubik{CB}
+%   \dnRubik{CBp}
+%  \end{supertabular}
 %
-% All  \rubikcube\ commands assume a 3x3x3 cube by default.
-% There are three primary command categories: (a)~\cmd{\Draw..} commands 
-% (which must always be used \textit{inside} a TikZ picture environment), 
-%  (b)~parameter-allocation' commands---e.g.,~\cmd{\RubikCubeSolved}---which can 
-%  be used either inside or outside  a TikZ environment),  
-%  and (c)~commands which can be used in ordinary text 
-% (e.g.,~|\rr{}| rotation commands).
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4.5cm}}
+%   \dntextRubik{MR}
+%   \dntextRubik{MRp}
+%   \dntextRubik{ML}
+%   \dntextRubik{MLp}
+%   \dntextRubik{MU}
+%   \dntextRubik{MUp}
+%   \dntextRubik{MD}
+%   \dntextRubik{MDp}
+%   \dntextRubik{MF}
+%   \dntextRubik{MFp}
+%   \dntextRubik{MB}
+%   \dntextRubik{MBp}
+%  \end{supertabular}
 %
-% Since \LaTeX\ commands have a maximum limit of only 9 parameters, 
-% it is necessary to use separate  `Face' and `Slice'  commands (see below)
-%   in order to accommodate  all 27 visible colours of a 3D~Rubik cube.
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4.5cm}}
+%   \dntextRubik{SR}
+%   \dntextRubik{SRp}
+%   \dntextRubik{SL}
+%   \dntextRubik{SLp}
+%   \dntextRubik{SU}
+%   \dntextRubik{SUp}
+%   \dntextRubik{SD}
+%   \dntextRubik{SDp}
+%   \dntextRubik{SF}
+%   \dntextRubik{SFp}
+%   \dntextRubik{SB}
+%   \dntextRubik{SBp}
+%  \end{supertabular}
+%
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4.5cm}}
+%   \dntextRubik{TR}
+%   \dntextRubik{TRp}
+%   \dntextRubik{TL}
+%   \dntextRubik{TLp}
+%   \dntextRubik{TU}
+%   \dntextRubik{TUp}
+%   \dntextRubik{TD}
+%   \dntextRubik{TDp}
+%   \dntextRubik{TF}
+%   \dntextRubik{TFp}
+%   \dntextRubik{TB}
+%   \dntextRubik{TBp}
+%  \end{supertabular}
 %
 %
+%    \subsection{The rubikfont}
+%     \label{sec:rubikfont}
+%
+%  For hieroglyph-related text we use the standard  Computer Modern Sans (cmss) 
+%  bold extended (bx) 10pt font for upper-case letters, and  the 8pt footnote size for lower-case  
+%   (see Section~\ref{sec:coderubikfont} for details).  This  font (rubikfont) 
+%   and the `prime' symbol (rubikprime) can be easily changed by `renewing' the three commands there.  
+%
+%  For example, to change to the somewhat `lighter' semi-bold extended (sbx) CM Sans (cmss) form
+%   one can simply include the following in the preamble (the FNS suffix stands for `footnotesize'):
+%\begin{verbatim}
+% \makeatletter
+% \renewcommand{\@rubikfont}{\fontsize{10}{12pt}\usefont{T1}{cmss}{sbx}{n}}
+% \renewcommand{\@rubikfontFNS}{\fontsize{8}{12pt}\usefont{T1}{cmss}{sbx}{n}}
+% \makeatother
+%\end{verbatim}
+% 
+%
+%    \subsubsection*{The `rubikprime' symbol}
+%     \label{sec:rubikprime}
+%
+% We currently  use the apostrophe for the prime symbol (see Section~\ref{sec:coderubikfont}),
+%  since the  maths \cmd{\prime} seems to be a bit too faint (especially since we need to use 
+% the `scriptstyle' size in this setting). However, users can 
+% easily make the Rubik bundle use the maths prime instead, by loading the following
+% in the preamble. 
+%\begin{verbatim}
+% \makeatletter
+% \renewcommand{\@rubikprime}{\raisebox{1.2pt}{\ensuremath{\scriptstyle{^\prime}}}}
+% \makeatother
+%\end{verbatim}
+%
+%
+%
+%    \section{Draw commands}
+%
+% A \cmd{\Draw..} command typesets  either a Rubik cube, cubie or a face 
+% or layer  using parameters set or defined via 
+% previous parameter-allocation commands (e.g.,~face colours, dimensions etc).
+% Note that those \cmd{\Draw..} commands which do take colours as arguments do not
+% update the cube's internal `colour state', but simply `paint' these colours.
+% 
+% It is important to distinguish between the \rubikcube\ package \cmd{\Draw..} commands 
+% and  TikZ \cmd{\draw..} commands.  \cmd{\Draw..} commands are implemented by the 
+% TikZ \cmd{\draw..} commands, and consequently  \cmd{\Draw..} commands can only be 
+% used \textit{inside} a TikZ  picture environment---and hence they can also be used safely in 
+% conjunction with the \cmd{\ShowCube} command, which itself uses a TikZ picture environment. 
+% See also   Section~\ref{sec:drawerrormessage} below..
+%
+%
+%
+%   \subsection[Error message]{\cmd{\Draw} error message}
+%   \label{sec:drawerrormessage}
+%
+% If a    \cmd{\Draw..} command is used \textit{outside} a 
+% TikZ picture  environment, then \LaTeX\  issues an
+%  ``Undefined control sequence'' error message, indicating 
+% that it is trying to draw  something using an undefined 
+% TikZ \cmd{\draw} command\,\footnote{Note that the TikZ  \cmd{\draw}  command 
+% uses a lower-case `d', while all \rubikcube\ commands start with an upper-case letter.}. 
+%
+% This is because all Rubik \cmd{\Draw..} commands achieve their effects by 
+% implementing a series of TikZ \cmd{\draw..} and other commands, all of which 
+% need to be inside a \texttt{tikzpicture} environment.
+%
+% For~example, if  the  command  \cmd{\DrawRubikCubeF} is used 
+% without a surrounding TikZ picture environment, 
+%  then something similar to  the following error message will be generated.
+%\begin{verbatim} 
+%! Undefined control sequence.
+%\DrawFlatUp ... }{#1}\pgfmathsetmacro {\uy }{#2}\draw
+%                                                      [line join=round,...
+%l.56 \DrawRubikCubeF
+%\end{verbatim}
+%
 %
-%    \subsection{Draw commands}
 %
-% A \cmd{\Draw..} command typesets  
-% either a Rubik cube, cubie or a layer  using parameters set or defined via 
-% previous parameter-allocation commands (eg~face colours, dimensions etc).
-% Furthermore, \cmd{\Draw..} commands can only be used \textit{inside} a TikZ 
-% picture environment  (see section~\ref{sec:drawerrormessage}).
 %
+%  \subsection{DrawRubikCube commands}
 %
 %   \DescribeMacro{\DrawRubikCubeXY}
-% This  command  draws Rubik cubes  in one of four 
-% orientations as denoted by the following terminal XY viewing-direction 
-% codes:  RU (RightUp),  RD (RightDown), LU (LeftUp),  LD (LeftDown). 
-%  For example, the command
+%   \DescribeMacro{\DrawRubikCubeF}
+%   \DescribeMacro{\DrawRubikCubeSF}
+% This  command  draws Rubik cubes  in one of four oblique 
+% orientations or configurations as denoted by the following terminal 
+% XY viewing-direction  codes:  RU~(RightUp),  RD~(RightDown), LU~(LeftUp), 
+% LD~(LeftDown); two additional terminal codes are F~(Flat) and SF~(Semi-Flat). 
+%  For~example, the command
 %  \begin{quote}
 %  \cmd{\DrawRubikCubeRU}
 %  \end{quote}
@@ -1323,7 +2208,7 @@
 %    \DrawRubikCubeRU 
 % \end{tikzpicture}%
 %\end{verbatim}
-% Note that these commands are equivalent to:
+% Note that the above commands are equivalent to:
 %\begin{verbatim}
 % \RubikCubeSolved
 % \ShowCube{3cm}{0.7}{\DrawRubikCubeRU} 
@@ -1347,42 +2232,32 @@
 % the xyz parameters  denote the face colours associated with each of 
 % the three axes. 
 %
-% For example, the  command    \cmd{\DrawCubieRU\{O\}\{Y\}\{G\}}   draws a 
+% For~example, the  command    \cmd{\DrawCubieRU\{O\}\{Y\}\{G\}}   draws a 
 %  single cubie as viewed  from the RightUp  direction, 
 % with face colours Orange (x-axis), Yellow (y-axis), Green (z-axis), as follows.
 % 
 % \medskip
 %
-% \begin{minipage}{1.35cm}
-% \begin{tikzpicture}[scale=1]
-% \DrawCubieRU{O}{Y}{G} 
-% \end{tikzpicture}%
-% \end{minipage}
+% \ShowCube{1.33cm}{1}{\DrawCubieRU{O}{Y}{G}} 
 %    \hspace{1cm}
 % \begin{minipage}{0.6\textwidth}
 %\begin{verbatim}
-% \begin{tikzpicture}[scale=1]
-%    \DrawCubieRU{O}{Y}{G} 
-% \end{tikzpicture}%
+% \ShowCube{1.33cm}{1}{\DrawCubieRU{O}{Y}{G}} 
 %\end{verbatim}
 % \end{minipage}
 % 
 % \medskip
 %
-% {\noindent}Since the front face is a unit 1cm and the width of the side approx 1/3cm, 
-%  and the scale factor =1, then the the minimum minipage width required for the cubie 
-% $=(1.33 \times 1) = 1.33$cm, and hence the  above commands are equivalent to 
-% \begin{verbatim}
-% \ShowCube{1.33cm}{1}{\DrawCubieRU{O}{Y}{G}}
-% \end{verbatim}
-%
+% {\noindent}Since the front face is 1~unit wide and the 2D width of the side approx 1/3~unit, 
+%  and the scale-factor =~1, then the  minipage width required for the cubie image 
+% $=(1.33 \times 1) = 1.33$cm.
 %
 % \begin{figure}[hbt]
 %   \centering
 % \ifpdf
-%    \includegraphics[height=4cm]{Rubik-doc-figC.pdf}
+%    \includegraphics[height=4cm]{rubik-doc-figC.pdf}
 %  \else
-% \includegraphics[height=4cm]{Rubik-doc-figC.eps}
+% \includegraphics[height=4cm]{rubik-doc-figC.eps}
 % \fi
 % \vspace{-5mm}\caption{\label{fig:cubiedydx}Cubie dy dx parameters} 
 % \end{figure}
@@ -1396,25 +2271,23 @@
 % \cmd{\Cubiedy\{\}} \\
 % \cmd{\Cubiedx\{\}} 
 % \end{quote}
-% as shown in the folowing example.
+% as shown in the following example.
 %
 % \bigskip
 %
-% \begin{minipage}{1.7cm}
-% \begin{tikzpicture}[scale=1]
-% \Cubiedy{0.4}
-% \Cubiedx{0.8}
-% \DrawCubieRU{O}{Y}{G} 
-% \end{tikzpicture}%
-% \end{minipage}
+% \ShowCube{1.7cm}{1}{%
+%   \Cubiedy{0.4}%
+%   \Cubiedx{0.8}%
+%   \DrawCubieRU{O}{Y}{G}% 
+%  }
 % \hspace{2cm}
 % \begin{minipage}{0.6\textwidth}
 %\begin{verbatim}
-% \begin{tikzpicture}[scale=1]
+% \ShowCube{1.7cm}{1}{%
 %   \Cubiedy{0.4}
 %   \Cubiedx{0.8}
 %   \DrawCubieRU{O}{Y}{G} 
-% \end{tikzpicture}%
+%  }
 %\end{verbatim}
 % \end{minipage}
 % 
@@ -1449,288 +2322,267 @@
 %  \textCubieLD{O}{Y}{G}  \ \  |\textCubieLD{O}{Y}{G}|  
 % \end{quote}
 % Note that these \cmd{\textCubieXY} commands are not influenced by the 
-% \cmd{\Cubiedy}, \cmd{\Cubiedx} commands as their size is preset for text use. 
-%
-%
-%     \subsubsection[Draw.. error message]{\cmd{\draw} error message}
-%
-% See also section~\ref{sec:drawerrormessage} regarding the error message associated with 
-% using a \cmd{\Draw...} command  \textit{outside}  a TikZ picture environment.
-%
+% \cmd{\Cubiedy}, \cmd{\Cubiedx} commands as their size is pre-set for text use. 
 %
-%  \subsection{Face commands}
-%   \label{sec:facecommands}
-%
-%  \DescribeMacro{\RubikFaceUp}
-%  \DescribeMacro{\RubikFaceDown}
-%  \DescribeMacro{\RubikFaceLeft}
-%  \DescribeMacro{\RubikFaceRight}
-%  \DescribeMacro{\RubikFaceFront}
-%  \DescribeMacro{\RubikFaceBack}
-% These  commands take nine colour arguments and  allocate   colours to the 
-% individual cubies  of a  Rubik cube face.
-% The ordering is isomorphic to the sequence 1--9, i.e.,~numbering the small 
-% squares 1-3~(top row, left to right), 4-6~(middle row, left to right), 
-% 7-9~(bottom row, left to right), as follows:
-% \begin{quote}
-% \fbox{
-% \begin{minipage}{1.6cm}
-% \#1 \#2 \#3 
 %
-% \#4 \#5 \#6
-%
-% \#7 \#8 \#9
-% \end{minipage}
-% }
-% \end{quote}
-% Conveniently, \LaTeX\ allows the colour arguments to be separated by spaces 
-% (e.g.,~separated in groups of three), or even spread across several 
-% lines (e.g.,~in a square block to resemble a 9-face) in order to 
-% make the command more visually intuitive, as in the following examples.
-% \begin{quote}
-%\begin{verbatim}
-% \RubikFaceUp{G}{B}{G}   {G}{W}{O}   {G}{O}{G}
-%
-% \RubikFaceFront{O}{W}{R}
-%                {W}{W}{W}
-%                {G}{W}{G}
 % 
-%\end{verbatim}
-% \end{quote}
-%
-%  \DescribeMacro{\RubikFaceUpAll}
-%  \DescribeMacro{\RubikFaceDownAll}
-%  \DescribeMacro{\RubikFaceLeftAll}
-%  \DescribeMacro{\RubikFaceRightAll}
-%  \DescribeMacro{\RubikFaceFrontAll}
-%  \DescribeMacro{\RubikFaceBackAll}
-% For convenience, each of these commands has an associated 
-% `\texttt{All}' command which allocates  the same colour to all the cubies 
-% on a 9-face  (i.e.,~only a single colour argument is required).
-%
-% If you want a particular face to be all grey, then one can 
-% either omit the particular `Face' command (since the 
-% default colour is grey), or  use  a `Face' command specifying the 
-% colour-code~X;  for example,  \cmd{\RubikFaceUpAll\{X\}}.
-% However, if you do use a Face command, then all of the command's 
-% colour arguments must be allocated, as otherwise you will generate a 
-% `missing parameter' error, and no colour will be 
-% allocated (i.e.,~you will see  a black-hole).
-% Use of these commands is shown in the following figure.
+%  \subsection{Flat commands}
+%  \label{sec:flatcommands}
 %
-% \bigskip
-% 
-% \begin{minipage}{2.8cm}
-% \RubikFaceUpAll{X}
-% \RubikFaceRightAll{R}
-% \RubikFaceFront{W}{Y}{G}
-%                {W}{Y}{G}
-%                {W}{Y}{G}
-% \begin{tikzpicture}[scale=0.7]
-% \DrawRubikCubeRU
-% \end{tikzpicture}%
-% \end{minipage}
-%    \hspace{5mm}
-% \begin{minipage}{0.6\textwidth}
-%\begin{verbatim}
-% \RubikFaceUpAll{X}
-% \RubikFaceRightAll{R}
-% \RubikFaceFront{W}{Y}{G}
-%                {W}{Y}{G}
-%                {W}{Y}{G}
-% \ShowCube{3cm}{0.7}{\DrawRubikCubeRU}
-% \end{verbatim}
-% \end{minipage}
-% 
+%  \DescribeMacro{\DrawFlatUp}
+%  \DescribeMacro{\DrawFlatDown}
+%  \DescribeMacro{\DrawFlatLeft}
+%  \DescribeMacro{\DrawFlatRight}
+%  \DescribeMacro{\DrawFlatFront}
+%  \DescribeMacro{\DrawFlatBack}
+%  These commands  \cmd{\DrawFlat..}\marg{x}\marg{y}  draw a `flat' (square) 
+%  representation of the current state of a specified face such that its 
+%  bottom left corner  is positioned at ($x$, $y$). 
+%  They are designed to supplement the \cmd{\DrawRubikCube...} commands and 
+%  allow hidden faces to be represented. 
+%  Each command (except \cmd{\DrawFlatFront}) takes two arguments, 
+%  namely the  X-coordinate  and Y-coordinate of the bottom left 
+%  corner of the  face.  This ($x$,$y$) pair allows the user to position
+%  the face. 
 %
-%       \subsection{RubikCubeSolved command}
-%    \label{sec:rubikcubesolved}
+%  Note that the Y-argument set for the \cmd{\DrawFlatLeft} 
+%  and \cmd{\DrawFlatRight} commands is not currently actioned 
+% (see Section~\ref{sec:drawflatxcommands}).
+%  This is because both the \textsc{left} and \textsc{right} faces, as used by the 
+% \cmd{\DrawRubikCubeSF} (Semi-Flat) command which incorporates the RU 
+%  view, require only Y=0. It is anticipated that this (x,y) facility 
+%  will  be fully  extended to  the left and right forms in a  later version.
+%
+%  Note also that the \cmd{\DrawFlatFront} command currently takes \textit{no} 
+%  arguments, since by definition the bottom left corner of this face is 
+%  always at (0,0),  and there seems to be no reason (just now) for 
+%  this face to have the  (x,y) facility.
+%
+%  \textsc{usage}:\ In the following example we use the command \verb!\DrawFlatBack{4}{1}! to
+%  append the \textsc{back} face to the side of a 3D  cube. Note that since 
+%  the coordinates of the bottom/back/right corner of the cube rendered by the 
+%  command \cmd{\DrawRubikCubeRU} is (4,1) 
+%  (see Section~\ref{sec:coordinates}), we can position the 
+%  lower/left corner of the \textsc{back} face at this point using the command
+%  \verb!\DrawFlatBack{4}{1}! as follows: 
 %
-%  \DescribeMacro{\RubikCubeSolved}
-% This command  sets all the face colours to that of a standard `solved' cube
-% and is equivalent to the following set of face commands
+%  \bigskip
+%  
+%  \begin{minipage}{0.4\textwidth}
+%  \centering
+%  \RubikCubeSolved
+%  \begin{tikzpicture}[scale=0.4]
+%  \DrawRubikCubeRU
+%  \DrawFlatBack{4}{1}
+%  \end{tikzpicture}%
+%  \end{minipage}
+%  \begin{minipage}{5cm}
 %\begin{verbatim}
-%  \RubikFaceUpAll{W}%
-%  \RubikFaceDownAll{Y}%
-%  \RubikFaceLeftAll{B}%
-%  \RubikFaceRightAll{G}%
-%  \RubikFaceFrontAll{O}%
-%  \RubikFaceBackAll{R}%
+%  \RubikCubeSolved
+%  \ShowCube{3cm}{0.4}{%
+%     \DrawRubikCubeRU
+%     \DrawFlatBack{4}{1}
+%  }
 %\end{verbatim}
-% as shown in the following semi-flat image.
-%
-% \bigskip
+%  \end{minipage}
+%    
+%  \bigskip
 %
-% \begin{minipage}{5cm}
-% \centering
-% \begin{tikzpicture}[scale=0.5]
-% \RubikCubeSolved
-% \DrawRubikCubeFlat
-% \end{tikzpicture}%
-% \end{minipage}
-% \begin{minipage}{0.5\textwidth}
+%  \DescribeMacro{\DrawRubikCubeF}
+%  This command  draws the completely flat (F) format of the cube, as  shown in the following example.
+%  
+%  \bigskip
+%  
+%  \begin{minipage}{0.4\textwidth}
+%  \centering
+%  \begin{tikzpicture}[scale=0.4]
+%  \RubikCubeSolved
+%  \DrawRubikCubeF
+%  \node (U) at (1.5, 4.5)   [black]{\small\textsf{U}};
+%  \node (D) at (1.5, -1.5)  [black]{\small\textsf{D}};
+%  \node (L) at (-1.5, 1.5)  [black]{\small\textsf{L}};
+%  \node (R) at (4.5, 1.5)   [black]{\small\textsf{R}};
+%  \node (F) at (1.5, 1.5)   [black]{\small\textsf{F}};
+%  \node (B) at (7.5, 1.5)   [black]{\small\textsf{B}};
+%  \end{tikzpicture}%
+%  \end{minipage}
+%  \begin{minipage}{5cm}
 %\begin{verbatim}
 %  \RubikCubeSolved
-%  \showcube{5cm}{0.5}{\DrawRubikCubeFlat}
+%  \ShowCube{5cm}{0.4}{\DrawRubikCubeF}
 %\end{verbatim}
-% \end{minipage}
-%
-% \bigskip
-%
-% Note that the width of the minipage above  is set to 5cm. This is derived from the fact 
-% that  the unscaled width of the semi-flat image is 10cm, and hence if
-% the TikZ scale factor is to be 0.5 then the minimum minipage width = $10 \times 0.5 = 5$cm
-% (see Section~\ref{sec:coordinates} for details).
-%
-% If other orientations of the solved cube are required, this can be easily achieved
-% using the \cmd{\RubikRotation} command (from the \texttt{RubikRotation} package).
-% For example, if one wants to show the solved cube upsidedown, then this format 
-% could be defined as follows (here we have used the rotations \rrx, \rrx, \rry, to 
-% invert the cube):
+%  \end{minipage}
+%  
+%  \bigskip
+%  
+%  The addition of  text (numbers or letters) in the faces is 
+%  straightforward---the origin of the 1-unit grid is located at the 
+%  bottom left corner of the \textsc{front} face (orange here). 
+%  The letters were placed using the following TikZ code inside the 
+%  TikZ picture environment.
+%  
 %\begin{verbatim}
-%\newcommand{\CubeUpSideDown}{\RubikCubeSolved\RubikRotation{x2,y}}
+%  \RubikCubeSolved
+%  \ShowCube{5cm}{0.4}{%
+%    \DrawRubikCubeF
+%    \node (U) at (1.5, 4.5)   [black]{\small\textsf{U}};
+%    \node (D) at (1.5, -1.5)  [black]{\small\textsf{D}};
+%    \node (L) at (-1.5, 1.5)  [black]{\small\textsf{L}};
+%    \node (R) at (4.5, 1.5)   [black]{\small\textsf{R}};
+%    \node (F) at (1.5, 1.5)   [black]{\small\textsf{F}};
+%    \node (B) at (7.5, 1.5)   [black]{\small\textsf{B}};
+%  }
 %\end{verbatim}
-% This command would then generate the following:
-%
-% \bigskip
+%  
+%  \DescribeMacro{\DrawRubikCubeSF}
+%  {\noindent}A useful `semi-flat' (SF) alternative format, which uses 
+%  the standard RU  view of the cube  and  appends the three hidden 
+%  sides (cf.,~Rokicki \textit{et~al.}, 2013),  is generated by the 
+%  command \cmd{\DrawRubikCubeSF} as follows.
+%  
+%  \bigskip
 %
-% \begin{minipage}{2.8cm}
-% \centering
-% \begin{tikzpicture}[scale=0.6]
-% \DrawNCubeAll{3}{O}{Y}{G}
-% \end{tikzpicture}%
-% \end{minipage}
-%    \hspace{5mm}
-% \begin{minipage}{0.6\textwidth}
+%  \begin{minipage}{5cm}
+%  \begin{tikzpicture}[scale=0.5]
+%  \RubikCubeSolved
+%  \DrawRubikCubeSF
+%  \node (B) at (5.5, 2.5)   [white]{\small\textsf{B}};
+%  \end{tikzpicture}%
+%  \end{minipage}
+%  \begin{minipage}{5cm}
 %\begin{verbatim}
-% \CubeUpSideDown
-% \ShowCube{2.4cm}{0.6}\DrawRubikCubeRU}
+%  \RubikCubeSolved
+%  \ShowCube{5cm}{0.5}{%
+%     \DrawRubikCubeSF
+%     \node (B) at (5.5, 2.5)  
+%              [white]{\small\textsf{B}};
+%  }
 %\end{verbatim}
-% \end{minipage}
-%
+%  \end{minipage}
+%  
 % \bigskip
 %
-%  Users can easily set their own alternative `solved'  face/colour configuration by `renewing' 
-%  the \cmd{\RubikCubeSolved} command as follows---remember to include the trailing \%  (note also
-%  that the colours  ROYGBWX are currently hardwired  so do not  use a different set 
-%  of uppercase letters).
-%\begin{verbatim}
-% \renewcommand{\RubikCubeSolved}{%
-%    \RubikFaceUpAll{..}%
-%    \RubikFaceDownAll{..}%
-%    \RubikFaceLeftAll{..}%
-%    \RubikFaceRightAll{..}%
-%    \RubikFaceFrontAll{..}%
-%    \RubikFaceBackAll{..}%
-% }
-%\end{verbatim} 
-%
-%
-%
-%       \subsection{RubikCubeGrey command}
-%       \label{sec:rubikcubegrey}
+% Note that even in this configuration it is straight-forward to
+% write text on the graphic, since the 2D width (on the page) of 
+% the green  \textsc{right} face is exactly 1-unit, and the 
+% bottom right-hand corner of the green face is raised exactly 1-unit
+% (see Figure~\ref{fig:cubesquaregraph}).
+% Consequently, since the origin of the  coordinate-grid is at the bottom left 
+% corner of the \textsc{front} face (the orange face here), the  coordinates 
+% of the centre of the  red \textsc{back} face are easily determined to be (5.5, 2.5). 
+%  
 %
-%  \DescribeMacro{\RubikCubeGrey}
-%  This command generates a 3x3x3 cube with no colours allocated except for the central
-%  cubie of each face, which takes the same colour configuration as defined for the 
-% \cmd{\RubikCubeSolved} command. 
-% This command, which is useful starting point when wanting to describe the movement of 
-% particular cubies, generates the following cube:
+%  \subsection{Face commands}
+%  \label{sec:facecommands}
+%
+%
+%  \DescribeMacro{\DrawFaceUp}
+%  \DescribeMacro{\DrawFaceDown}
+%  \DescribeMacro{\DrawFaceLeft}
+%  \DescribeMacro{\DrawFaceRight}
+%  \DescribeMacro{\DrawFaceFront}
+%  \DescribeMacro{\DrawFaceBack}
+%  \DescribeMacro{\DrawFaceUpSide}
+%  \DescribeMacro{\DrawFaceDownSide}
+%  \DescribeMacro{\DrawFaceLeftSide}
+%  \DescribeMacro{\DrawFaceRightSide}
+%  \DescribeMacro{\DrawFaceFrontSide}
+%  \DescribeMacro{\DrawFaceBackSide}
+% These commands draw the current state of a specified  face 
+% (e.g.,~\cmd{\DrawFaceUp}), or the face and all the associated side-bars
+% (e.g.,~\cmd{\DrawFaceUpSide}).
+% \textsc{Note}: these  commands  do \textsc{not} take any 
+% arguments---for code see Section~\ref{sec:drawfacecode}.
 %
-% \bigskip
+% In the following example we use the \cmd{\DrawFlatUpSide} command to
+%  draw the \textsc{up} face and all its side-bars of a cube  having 
+% a `solved' configuration.
 %
-% \RubikCubeGrey
-% \ShowCube{3cm}{0.5}{\DrawRubikCubeRU}
-%    \hspace{5mm}
-% \begin{minipage}{0.6\textwidth}
+%  \bigskip
+%  
+%  \begin{minipage}{0.4\textwidth}
+%  \centering
+%  \RubikCubeSolved
+%  \begin{tikzpicture}[scale=0.4]
+%  \DrawFaceUpSide
+%  \end{tikzpicture}%
+%  \end{minipage}
+%  \begin{minipage}{5cm}
 %\begin{verbatim}
-% \RubikCubeGrey
-% \ShowCube{3cm}{0.5}{\DrawRubikCubeRU}
+%  \RubikCubeSolved
+%  \ShowCube{1.6cm}{0.4}{%
+%     \DrawFaceUpSide
+%  }
 %\end{verbatim}
-% \end{minipage}
-%
-% \bigskip
-%  Users can easily set their own alternative  face/colour configuration by `renewing' 
-% the \cmd{\RubikCubeGrey} command along the lines shown above (the code is in Section~\ref{sec:codegrey}). 
+%  \end{minipage}
 %
+% \vspace{1cm}
 %
 %
-%    \subsection{Slice commands}
-%   \label{sec:slicecommands}
-%
-%  \DescribeMacro{\RubikSliceTopX}
-%  \DescribeMacro{\RubikSliceMiddleX}
-%  \DescribeMacro{\RubikSliceBottomX}
-%  These three commands  allocate the six visible cubie colours associated with  a
-%   \textit{horizontal}  slice of a Rubik cube. 
-% There are three pairs of  Slice commands; one pair 
-% (Left view \& Right view) for each of the horizontal  slices Top, Middle, Bottom.
-% The six colour arguments  associated with a given slice run in sequence 
-% from left to right irrespective of the viewpoint, e.g.,~\#1 \#2 \#3   \#4 \#5 \#6.
-%
-% Since the viewpoint of the Rubik cube (from the Right or from the Left) 
-% influences which face the colours are associated with, it is necessary 
-% to have the view (R or L) specified in the command name.
+%      \subsection[NCube]{NCube (NxNxN)}
+%      \label{sec:NCube}
+% 
+%  \DescribeMacro{\DrawNCubeAll} 
+%  An `NCube' is  a solved NxNxN cube drawn from the RU direction; 
+%  (i.e.,~only shows faces \textsc{up}, \textsc{front}, \textsc{right}). 
+%  The cubie colours of each face are All the same.
+%  \begin{quote}
+%    \cmd{\DrawNCubeAll\{N\}\{Xcolour\}\{Ycolour\}\{Zcolour\}}.
+%  \end{quote}
+%  This command takes four ordered parameters (N, X, Y, Z)---the number 
+%  (integer; $N>0$) of cubies along an edge, followed by three face 
+%  colours in XYZ order.
+%  Since the viewpoint is only from the RU direction, the  three colour 
+%  parameters are: X(Right), Y(Up), Z(Front).
+%  
+%  \bigskip
+%  
+%  \begin{minipage}{0.3\textwidth}
+%  \begin{tikzpicture}[scale=0.5]
+%     \DrawNCubeAll{5}{O}{Y}{G}
+%  \end{tikzpicture}%
+%  \end{minipage}
+%  \begin{minipage}{0.5\textwidth}
+%\begin{verbatim}
+% \ShowCube{3.5cm}{0.5}{\DrawNCubeAll{5}{O}{Y}{G}}
+%\end{verbatim}
+%  \end{minipage}
 %
-% The format of the `slice' command is shown in the following example.
-% The Rubik  cube is shown from  the LeftDown (LD) view 
-% and consequently  each of the `slice' commands in this
-% particular example  ends in L, consistent with 
-% the final \cmd{\DrawRubikCubeLD} command.
 %
-% Note that the two legacy `Equator' versions (now replaced by `Middle') 
-% are retained to allow backward compatibility. 
 %
-% \bigskip
 %
-% \begin{minipage}{2.8cm}
-% \centering
-% \RubikFaceDownAll{Y}
-% \RubikSliceTopL    {G}{G}{G} {R}{R}{R}
-% \RubikSliceMiddleL {R}{R}{R} {B}{B}{B}
-% \RubikSliceBottomL {O}{O}{O} {G}{G}{G}
-% \begin{tikzpicture}[scale=0.7]
-% \DrawRubikCubeLD
-% \end{tikzpicture}%
-% \end{minipage}
-%    \hspace{5mm}
-% \begin{minipage}{0.6\textwidth}
-%\begin{verbatim}
-%    \RubikFaceDownAll{Y}
-%    \RubikSliceTopL     {G}{G}{G} {R}{R}{R}
-%    \RubikSliceMiddleL  {R}{R}{R} {B}{B}{B}
-%    \RubikSliceBottomL  {O}{O}{O} {G}{G}{G}
-%    \ShowCube{3cm}{0.7}{\DrawRubikCubeLD}
-%\end{verbatim}
-% \end{minipage}
 %
+%  \subsection{LayerFace}
+%   \label{sec:layerface}
 %
-%  \subsection{LayerFace \& LayerSide commands}
-%  \label{sec:layerface}
+%  While a cube has faces and layers, a layer has a face (the face you are looking 
+%  at or drawing) and  four sides (consisting of the nine  side facelets of the 
+%  associated cubies). 
+%  The two `Layer' commands described here are   intended  for drawing  final layer 
+%  configurations from `scratch' without any prior configuration information.
 %
-%  These commands are   intended  for drawing  final layer 
-%  configurations (i.e.,~typically using the yellow face in the  \textsc{up} position)
-%  with or without the associated side faces of the cubies of the top layer
-% (see also the \cmd{\DrawFlatUpSide} command in Section~\ref{sec:flatcommands}) 
+%  Typically, we might wish to show the yellow face in 
+%  the  \textsc{up} position,  with or without the associated side faces of the 
+%  cubies of this layer.
+%  Of course, if we already know the rotation history from some initial configuration,
+%  it would be much simpler just to invoke the \cmd{\RubikRotation} command and then use the  
+%  \cmd{\DrawFlatUpSide} command  (see Section~\ref{sec:flatcommands}).
 %
-%  \subsubsection{LayerFace}
 %
 %  \DescribeMacro{\DrawRubikLayerFace}
-%  This LayerFace command  draws a  simple  Rubik cube 3x3 face and allocates colours
-%  to the  9~cubies.
-%  The command takes nine ordered colour arguments.
-%  Their use is illustrated in the following example, which shows  a yellow cross configuration.
+%  \DescribeMacro{\DrawRubikLayerFaceAll}
+%  These two LayerFace commands  draw a  simple   3x3 face and allocate colours
+%  to the  9~facelets.
+%  The \cmd{\DrawRubikLayerFace} command takes nine ordered colour arguments.
+%  The command is illustrated in the following example, which shows  a yellow cross configuration.
 %  
 %  \bigskip
 %
-%  \begin{minipage}{2.5cm}
-%  \centering
-%  \begin{tikzpicture}[scale=0.7]
-%  \DrawRubikLayerFace{X}{Y}{X}
-%                     {Y}{Y}{Y}
-%                     {X}{Y}{X}
-%  \end{tikzpicture}%
-%  \end{minipage}
+%  \ShowCube{2.1cm}{0.7}{%
+%    \DrawRubikLayerFace{X}{Y}{X}
+%                       {Y}{Y}{Y}
+%                       {X}{Y}{X}
+%    }%
 %  \hspace{1cm}
 %  \begin{minipage}{0.6\textwidth}
 %\begin{verbatim}
@@ -1738,35 +2590,34 @@
 %     \DrawRubikLayerFace{X}{Y}{X}
 %                        {Y}{Y}{Y}
 %                        {X}{Y}{X}
-%  }
+%     }
 %\end{verbatim}
 %  \end{minipage}
 %
-% \medskip
-%
-%      \subsubsection[Draw.. error message]{\cmd{\draw} error message}
+% \bigskip
 %
-% See also section~\ref{sec:drawerrormessage} regarding the error message associated with 
-% using a \cmd{\Draw...} command  \textit{outside}  a TikZ picture environment.
+%  {\noindent}The \cmd{\DrawRubikLayerFaceAll} command takes a single colour argument, and paints 
+% the whole face the same colour.
 %
 %  \medskip
 %
-%    \subsubsection{LayerSide}
-%     \label{sec:layerside}
+%    \subsection{LayerSide (sidebars)}
+%     \label{sec:layerside} \label{sec:sidebars}
 % 
 %  \DescribeMacro{\DrawRubikLayerSideXYp}
 %  LayerSide commands  draw the associated side colours  of  
-%  the top layer   as  small rectangular sidebars.
-%  The LayerSide commands  adopt a three-letter XYp \textbf{position} notation 
+%  the layer   as  small rectangular sidebars.
+%  The LayerSide command  adopts a three-letter XYp \textbf{position} notation 
 %   where the  XY pair define the location (X:[Left \verb!|! Middle \verb!|! Right]; 
-%  Y:[Top \verb!|! Middle \verb!|! Bottom]) of a particular cubie in the layer face.
+%  Y:[Top \verb!|! Middle \verb!|! Bottom]) of a particular cubie in the layer face,
+%  as depicted in Figure~\ref{fig:facenotation}.
 %
 %  \begin{figure}[hbt]
 %     \centering
 %  \ifpdf
-%     \includegraphics[height=3cm]{Rubik-doc-figD.pdf}
+%     \includegraphics[height=3cm]{rubik-doc-figD.pdf}
 %  \else
-%  \includegraphics[height=3cm]{Rubik-doc-figD.eps}
+%  \includegraphics[height=3cm]{rubik-doc-figD.eps}
 %  \fi
 %  \vspace{-5mm}\caption{\label{fig:facenotation}LayerSide rotation-codes } 
 %  \end{figure}
@@ -1782,7 +2633,7 @@
 %  Various different LayerSide commands are available: those for  
 %  drawing a single colour side bar, and   others for facilitating  
 %  drawing all 12 side bars.
-%     For example, \textit{either} of the following commands 
+%     For~example, \textit{either} of the following commands 
 %
 %  \begin{quote}
 %\begin{verbatim}
@@ -1805,9 +2656,9 @@
 %\end{verbatim}
 %  \end{quote}
 %  where the T and B forms require the colour parameters to be in left-right 
-%  horizontal order (eg, left, middle, right),
+%  horizontal order (e.g.,~left, middle, right),
 %  while the L and R forms require the colour parameters to be in top-down 
-%  vertical order (eg, top, middle, bottom).
+%  vertical order (e.g.,~top, middle, bottom).
 %  Note that this means that the colour parameters of the  L and R commands 
 %  can (if required) then be positioned intuitively (vertically) as follows:
 %  \begin{quote}
@@ -1864,11 +2715,9 @@
 %     \DrawRubikLayerSideR{O}{B}{R}
 %     \DrawRubikLayerSideB{R}{G}{O}
 %  
-%     \node (LT) at (0.5, 2.5) 
-%                [red]{\small\textsf{LT}};
-%     \node (LM) at (0.5, 1.5)  
-%                [red]{\small\textsf{LM}};
-%  }
+%     \node (LT) at (0.5, 2.5) [red]{\small\textsf{LT}};
+%     \node (LM) at (0.5, 1.5) [red]{\small\textsf{LM}};
+%     }
 %\end{verbatim}
 %  \end{minipage}
 %  
@@ -1903,21 +2752,19 @@
 %                          {R}   {O}
 %                          {Y}   {O}
 %     \DrawRubikLayerSideB {O}{G}{G}  
-%  }
+%     }
 %\end{verbatim}
 %  \end{minipage}
 %  
 %  \bigskip
 %
-%  \DescribeMacro{\DrawFlatUpSide}
-% \textsc{important note}: If the  colour configuration of the  \textit{whole} 
-% cube is already known to the system (i.e.,~it has been specified before,
-%  and (possibly) been manipulated using the \cmd{\RubikRotation..}  command 
+%  \DescribeMacro{\DrawFaceUpSide}
+% \textsc{important note}: If the  colour configuration of the  layer shown above 
+% is already known to the system (i.e.,~it has been specified before,
+%  and (possibly) been manipulated using the \cmd{\RubikRotation}  command 
 % from \textsc{rubikrotation} package), then the above figure could be 
-% drawn much more simply using just the single \cmd{\DrawFlatUpSide} command, 
-% as described in  Section~\ref{sec:flatcommands}. In short, using  the 
-% \texttt{rubikrotation} package to keep track of the Rubik cube configuration makes
-%  drawing these images  considerably simpler.
+% drawn much more simply using just the single \cmd{\DrawFaceUpSide} command, 
+% as described in  Section~\ref{sec:facecommands}. 
 %  
 %  \bigskip
 %
@@ -1930,14 +2777,15 @@
 %  These sidebar values (decimal values $\geq 0$; no units) can be 
 %  changed from their default values using the three commands.
 %  \begin{quote}
-%  \cmd{\RubikSideBarWidth\{\}}\\
-%  \cmd{\RubikSideBarLength\{\}}\\
-%  \cmd{\RubikSideBarSep\{\}}
+%  \cmd{\RubikSideBarWidth\{\}}\hspace{35.751pt}(default = 0.3)\\
+%  \cmd{\RubikSideBarLength\{\}}\hspace{30pt}(default = 1.0)\\
+%  \cmd{\RubikSideBarSep\{\}}\hspace{46.251pt}(default = 0.3)
 %  \end{quote}
 %  Values set in the document preamble will apply globally, while values 
 %  set within a TikZ picture environment will apply only locally to that 
 %  particular environment, as shown in the following example where we have 
-%  set both the sidebar width and length to 0.7.
+%  set both the sidebar width and length to 0.7 in position MTy using the command 
+%   \verb!\DrawRubikLayerSideMTy{G}! (for the MTy code see Figure~\ref{fig:facenotation}).
 %  
 %  \bigskip
 %
@@ -1965,7 +2813,7 @@
 %     \RubikSideBarWidth{0.7}
 %     \RubikSideBarLength{0.7}
 %     \DrawRubikLayerSideMTy{G}
-%   }
+%     }
 %\end{verbatim}
 %  \end{minipage}
 %  
@@ -1979,12 +2827,11 @@
 %  Since the \textsc{front} face  drawn using  the \cmd{\DrawRubikCube} command is 
 %  identical with that drawn using the \cmd{\DrawLayerFace} command it 
 %  follows that LayerSide commands can also be used in conjunction with 
-%  the \textsc{front} face drawn using  \cmd{\DrawRubikCube} command, as 
-%  shown in the following example. Note that in this example we have used the 
-% \cmd{\ShowCubeF} command as an exercise to implement the fbox and reveal
-% the extent of the  surrounding white space associated with a minipage width of
-% 3.5cm ($=5 \times 0.7$) ---showing that a sidebar increases the image width by about 
-% 0.5 the width of a cubie.
+%  the \textsc{front} face drawn using  \cmd{\DrawRubikCube} command. This  
+%  shown in the following example, where we have used the 
+% \cmd{\ShowCubeF} command as an exercise (to implement the fbox) and reveal
+% the extent of the  surrounding white space associated with the minipage width of
+% 3.5cm ($=5 \times 0.7$).
 %  
 %  \bigskip
 %  
@@ -2025,233 +2872,219 @@
 %     \DrawRubikCubeRU 
 %     \DrawRubikLayerSideL{G}{B}{R}
 %     \DrawRubikLayerSideB{R}{G}{O}
-%   }
+%     }
 %\end{verbatim}
 %  \end{minipage}
 %  
 %  \bigskip
 %  
-%  {\noindent}Note that since using a left or a right \cmd{\DrawRubikLayerSide}  
-%  command in conjunction with a \cmd{\DrawRubikCube} command will necessarily 
-%  increase the width of the image, one may also have to adjust the width of 
-%  the associated minipage. 
-%  
-% \pagebreak
+%  Since using  left and/or  right sidebars (e.g.,~\cmd{\DrawRubikLayerSide})
+%   in conjunction with  a \cmd{\DrawRubikCube} command, will increase 
+%  the width of the image, one may also have to adjust the width of 
+%  the associated minipage.  Note that the width of a 2D oblique view of the cube 
+% is 4~units (= width of 4~cubies). With the default sidebar width and sep settings 
+% (see above)  one sidebar increases the  2D cube image width by 0.6\,units (= 0.3 + 0.3). 
+% Sidebars on both sides increase the width by 1.2\,units. Note also that setting 
+% both the sidebar width and separation to 0.25\,units has the convenience that 
+% the 2D width of a cube face $+$ left and right sidebars (e.g.,~using \cmd{\DrawFaceUpSide})
+%  is then exactly 5\,units. 
+%
+%
+%
+%
+%   \section[ShowSequence command]{\cmd{\ShowSequence} command}
+%   \label{sec:showsequence}
+%
+% \DescribeMacro{\ShowSequence}
+% \DescribeMacro{\ShowSequenceF}
+% \DescribeMacro{\ShowSequencef}
+% The  \cmd{\ShowSequence}\marg{separator}\marg{font-code}\marg{sequence}  command 
+% typesets a comma-separated sequence of rotation  
+% codes---for code see Section~\ref{sec:codeshowsequence}.
+% Appending an `F' to the command-name (\cmd{\ShowSequenceF}) results in an fbox about
+% the whole output (cf.~the \cmd{\ShowCubeF} command). 
+% Appending an `f' to the command-name (\cmd{\ShowSequencef}) results in an fbox about
+% each element in the output (these two forms can be helpful when checking white space). 
+%
+% The \cmd{\ShowSequence} command takes three mandatory arguments: 
+% the first is the separator  (\verb!#1!), 
+% the second is  the font or style code (\verb!#2!), 
+% and third is a comma-separated  sequence of Rubik  rotation codes (|#3|).
+%
+% The separator (e.g.,~comma) used for typesetting the sequence can be specified 
+% (or just omitted---i.e.,~an empty bracket);
+% the sequence can be either a named sequence (i.e.,~encoded as a macro) or just a 
+% comma separated sequence of  rotation codes.
 % 
-%  \subsection{Flat commands}
-%  \label{sec:flatcommands}
+% \noindent\textsc{usage}:
+% The following command  displays the rotation sequence  F, R, U, Rp, Up, using 
+% the \verb!\rr! encoding and  comma \& space separated.
 %
-%  \DescribeMacro{\DrawFlatUp}
-%  \DescribeMacro{\DrawFlatDown}
-%  \DescribeMacro{\DrawFlatLeft}
-%  \DescribeMacro{\DrawFlatRight}
-%  \DescribeMacro{\DrawFlatFront}
-%  \DescribeMacro{\DrawFlatBack}
-%  These commands  \cmd{\DrawFlat..}\marg{x}\marg{y}  draw a `flat' (square) 
-%  representation of a  specified face such that its bottom left corner 
-%  is positioned at ($x$, $y$). 
-%  They are designed to supplement the \cmd{\DrawRubikCube...} commands and 
-%  allow hidden faces to be represented. 
-%  Each command (except \cmd{\DrawFlatFront}) takes two arguments, 
-%  namely the  X-coordinate  and Y-coordinate of the bottom left 
-%  corner of the  face.  This ($x$,$y$) pair allows the user to position
-%  the face. 
+% \medskip
 %
-%  Note that the Y-argument set for the \cmd{\DrawFlatLeft} 
-%  and \cmd{\DrawFlatRight} commands is not currently actioned 
-% (see Section~\ref{sec:drawflatxcommands}),
-%  since both the \textsc{left} and \textsc{right} faces as used by the 
-% \cmd{\DrawRubikCubeFlat} command---since this shows the RU view---requires only Y=0
-%  (this (x,y) facility will  be fully extended to  the left and right forms in a 
-%  later version).
-%  Note also that the \cmd{\DrawFlatFront} command currently takes no arguments,
-%  since by definition the bottom left corner of this face is always at (0,0), 
-%  and there seems to be no reason (just now) for this face to have the 
-%  (x,y) facility.
+% \verb!\ShowSequence{,\ }{\rr}{F,R,U,Rp,Up}! \ \ $\rightarrow$ \ \ \ShowSequence{,\ }{\rr}{F,R,U,Rp,Up}
 %
-%  In the following example we use the command \verb!\DrawFlatBack{4}{1}! to
-%  append the \textsc{back} face to the side of a 3D  cube. Note that since 
-%  the coordinates of the bottom/back/right corner of the cube rendered by the 
-%  command \cmd{\DrawRubikCubeRU} is (4,1) 
-%  (see Section~\ref{sec:coordinates}), we can position the 
-%  lower/left corner of the \textsc{back} face at this point using the command
-%  \verb!\DrawFlatBack{4}{1}! as follows: 
+% \medskip
 %
-%  \bigskip
-%  
-%  \begin{minipage}{0.4\textwidth}
-%  \centering
-%  \RubikCubeSolved
-%  \begin{tikzpicture}[scale=0.4]
-%  \DrawRubikCubeRU
-%  \DrawFlatBack{4}{1}
-%  \end{tikzpicture}%
-%  \end{minipage}
-%  \begin{minipage}{5cm}
-%\begin{verbatim}
-%  \RubikCubeSolved
-%  \ShowCube{3cm}{0.4}{%
-%     \DrawRubikCubeRU
-%     \DrawFlatBack{4}{1}
-%  }
-%\end{verbatim}
-%  \end{minipage}
-%  
-%  \bigskip
+% Remember that if you want a  very long  sequence to break automatically 
+% at the line-ends, then you need to include at least one space between 
+% the sequence elements, either with or without a comma; for this the 
+% separator argument needs to include a space, i.e.,~something like 
+% \verb!{,\ }! or \verb!{\ }!  or just \verb!{ }! perhaps.
 %
 %
-%  \DescribeMacro{\DrawFlatUpSide}
-%  \DescribeMacro{\DrawFlatDownSide}
-%  \DescribeMacro{\DrawFlatLeftSide}
-%  \DescribeMacro{\DrawFlatRightSide}
-%  \DescribeMacro{\DrawFlatFrontSide}
-%  \DescribeMacro{\DrawFlatBackSide}
-% These commands draw a face and all the associated side facelets. 
-% In the following example we use the \cmd{\DrawFlatUpSide} command to
-%  draw the \textsc{up} face and all its side-bars of a cube  having 
-% a `solved' configuration.
+% For~example, the following commands typeset the comma-separated 
+% rotation sequence U,D,Lp,R  using different separators and fonts. 
+% For convenience, we start by encoding  the sequence as the macro \verb!\myseq!.
 %
 %
-%  \bigskip
-%  
-%  \begin{minipage}{0.4\textwidth}
-%  \centering
-%  \RubikCubeSolved
-%  \begin{tikzpicture}[scale=0.4]
-%  \DrawFlatUpSide
-%  \end{tikzpicture}%
-%  \end{minipage}
-%  \begin{minipage}{5cm}
-%\begin{verbatim}
-%  \RubikCubeSolved
-%  \ShowCube{1.6cm}{0.4}{%
-%     \DrawFlatUpSide
-%  }
-%\end{verbatim}
-%  \end{minipage}
-%  
-%  \bigskip
+% \newcommand{\myseq}{U,D,Lp,R}
 %
-%  \DescribeMacro{\DrawRubikFlat}
-%  This command  draws the completely flat format of the cube, as  shown in the following example.
-%  
-%  \bigskip
-%  
-%  \begin{minipage}{0.4\textwidth}
-%  \centering
-%  \begin{tikzpicture}[scale=0.4]
-%  \RubikCubeSolved
-%  \DrawRubikFlat
-%  \node (U) at (1.5, 4.5)   [black]{\small\textsf{U}};
-%  \node (D) at (1.5, -1.5)  [black]{\small\textsf{D}};
-%  \node (L) at (-1.5, 1.5)  [black]{\small\textsf{L}};
-%  \node (R) at (4.5, 1.5)   [black]{\small\textsf{R}};
-%  \node (F) at (1.5, 1.5)   [black]{\small\textsf{F}};
-%  \node (B) at (7.5, 1.5)   [black]{\small\textsf{B}};
-%  \end{tikzpicture}%
-%  \noindent\strut\hspace{5mm}\texttt{$\backslash$DrawRubikFlat}
-%  \end{minipage}
-%  \begin{minipage}{5cm}
-%\begin{verbatim}
-%  \RubikCubeSolved
-%  \ShowCube{5cm}{0.4}{\DrawRubikFlat}
-%\end{verbatim}
-%  \end{minipage}
-%  
-%  \bigskip
-%  
-%  The addition of  text (numbers or letters) in the faces is 
-%  straightforward---the origin of the 1-unit grid is located at the 
-%  bottom left corner of the front face (orange here). 
-%  The letters were placed using the following TikZ code inside the 
-%  TikZ picture environment.
-%  
-%\begin{verbatim}
-%  \RubikCubeSolved
-%  \ShowCube{5cm}{0.4}{%
-%    \DrawRubikFlat
-%    \node (U) at (1.5, 4.5)   [black]{\small\textsf{U}};
-%    \node (D) at (1.5, -1.5)  [black]{\small\textsf{D}};
-%    \node (L) at (-1.5, 1.5)  [black]{\small\textsf{L}};
-%    \node (R) at (4.5, 1.5)   [black]{\small\textsf{R}};
-%    \node (F) at (1.5, 1.5)   [black]{\small\textsf{F}};
-%    \node (B) at (7.5, 1.5)   [black]{\small\textsf{B}};
-%  }
-%\end{verbatim}
-%  
-%  \DescribeMacro{\DrawRubikCubeFlat}
-%  {\noindent}A useful `semi-flat' alternative format, which uses 
-%  the standard RU  view of the cube  and  appends the three hidden 
-%  sides (see Rokicki \textit{etal.}, 2013),  is generated by the 
-%  command \cmd{\DrawRubikCubeFlat} as follows.
-%  
-%  \bigskip
+% \medskip\noindent\verb!\newcommand{\myseq}{U,D,Lp,R}!
 %
-%  \begin{minipage}{5cm}
-%  \begin{tikzpicture}[scale=0.5]
-%  \RubikCubeSolved
-%  \DrawRubikCubeFlat
-%  \node (B) at (5.5, 2.5)   [white]{\small\textsf{B}};
-%  \end{tikzpicture}%
-%  \end{minipage}
-%  \begin{minipage}{5cm}
-%\begin{verbatim}
-%  \RubikCubeSolved
-%  \ShowCube{5cm}{0.5}{%
-%     \DrawRubikCubeFlat
-%     \node (B) at (5.5, 2.5)  
-%              [white]{\small\textsf{B}};
-%  }
-%\end{verbatim}
-%  \end{minipage}
-%  
-% \bigskip
+% \medskip\noindent\verb!\ShowSequence{,}{\texttt}{\myseq}! \ $\longrightarrow$ \  \ShowSequence{,}{\texttt}{\myseq}
 %
-% Note that even in this configuration it is straight-forward to
-% write text on the graphic, since the width (on the page) of 
-% the green  \textsc{right} face is exactly 1-unit, and the 
-% bottom right-hand corner of the green face is raised exactly 1-unit
-% (see Figure~\ref{fig:cubesquaregraph}).
-% Consequently, since the origin of the grid is at the bottom left 
-% corner of the front face, the  coordinates of the center of the 
-% red \textsc{back} face is (5.5, 2.5). 
-%  
-%      \section[NCube]{NCube (NxNxN)}
-%      \label{sec:NCube}
+% \medskip\noindent\verb!\ShowSequence{,}{\rr}{\myseq}! \ $\longrightarrow$ \  \rr{U},\rr{D},\rr{Lp},\rr{R} 
+%
+% \medskip\noindent\verb!\ShowSequence{}{\rrh}{\myseq}! \ $\longrightarrow$ \  \rrh{U}\rrh{D}\rrh{Lp}\rrh{R}
+%
+% \medskip\noindent\verb!\ShowSequence{\ }{\rrh}{\myseq}! \ $\longrightarrow$ \  \rrh{U}\ \rrh{D}\ \rrh{Lp}\ \rrh{R}
 % 
-%  \DescribeMacro{\DrawNCubeAll} 
-%  An `NCube' is  a solved NxNxN cube drawn from the RU direction; 
-%  (i.e.,~only shows faces \textsc{up}, \textsc{front}, \textsc{right}). 
-%  The cubie colours of each face are All the same.
-%  \begin{quote}
-%    \cmd{\DrawNCubeAll\{N\}\{Xcolour\}\{Ycolour\}\{Zcolour\}}.
-%  \end{quote}
-%  This command takes four ordered parameters (N, X, Y, Z)---the number 
-%  (integer; $N>0$) of cubies along an edge, followed by three face 
-%  colours in XYZ order.
-%  Since the viewpoint is only from the RU direction, the  three colour 
-%  parameters are: X(Right), Y(Up), Z(Front).
-%  
-%  \bigskip
-%  
-%  \begin{minipage}{0.3\textwidth}
-%  \begin{tikzpicture}[scale=0.5]
-%     \DrawNCubeAll{5}{O}{Y}{G}
-%  \end{tikzpicture}%
-%  \end{minipage}
-%  \begin{minipage}{0.5\textwidth}
+% \medskip\noindent\verb!\ShowSequence{,\ }{\textRubik}{\myseq}! \ $\longrightarrow$ \  \textRubik{U},\ \textRubik{D},\
+% \textRubik{Lp},\ \textRubik{R}
+% 
+% 
+% \subsection*{Trailing digits}
+%
+%  Note that the fonts denoted by \verb!\rr!, \verb!\rrh!, \verb!\Rubik! 
+%  and \verb!\textRubik!  will fail for  rotation codes which 
+%  have a trailing digit, e.g.,~R2, Dp3 (so-called `short' codes), since the 
+%  \verb!\ShowSequence! macro currently only reads the whole string  between pairs of 
+%  commas (i.e.,~it does not interpret each string). However, the typewriter font \verb!\texttt! 
+%  does work correctly in this case, as you would expect. 
+% 
+%  An effective `work-around' for this limitation  is provided by the \verb!\RubikRotation{}! 
+%  command\,\footnote{Using the \texttt{--shell-escape} command-line option
+%  with the \LaTeX\ engine---see Section~\ref{sec:rubikrotation}.} 
+%  (part of the \textsc{rubikrotation} package), since this returns  (via the Perl program  
+%  \texttt{rubikrotation.pl}) an extended (`long') form of a given sequence in which 
+%  any `short' rotation codes are converted into their separate (atomic) long-form rotation codes; 
+%  the associated string  is  \verb!\SequenceLong!. 
+%  In fact  three different forms of the sequence are returned, as shown below.
+% 
+%  For~example, consider the following short-form sequence  L,R,D2,L3, and denote 
+%  it as `seqA' as follows: \verb!\newcommand{\seqA}{[seqA],L,R,D2,L3,<test>}!.
+%  In this case  D2,L3, and the name `seqA'  fail to be typeset when using 
+%  the \verb!\rr! font  with the \verb!\ShowSequence! command as follows:
+% 
+%  \newcommand{\seqA}{[seqA],L,R,D2,L3,<test>}
+% 
+%  \medskip\noindent\verb!\newcommand{\seqA}{[seqA],L,R,D2,L3,<test>}!
+%
+% \medskip\noindent\verb!\ShowSequence{,}{\texttt}{\seqA}! \ $\longrightarrow$ \  \ShowSequence{,}{\texttt}{\seqA}
+%
+% \medskip\noindent\verb!\ShowSequence{,}{\rr}{\seqA}! \ $\longrightarrow$ \  \ShowSequence{,}{\rr}{\seqA}
+% 
+% \medskip
+% 
+% However, if we now run the command \verb!\RubikRotation{\seqA}! we shall then have 
+% at our disposal the following four  strings:
+%
+% \medskip
+%
+% \verb!\SequenceInfo   = ! test
+%
+% \verb!\SequenceName   = ! seqA
+% 
+% \verb!\SequenceShort  = ! L,R,D2,L3
+% 
+% \verb!\SequenceLong   = ! L,R,D,D,L,L,L
+%
+% \medskip
+% 
+% {\noindent}and therefore have full control over  typesetting    rotation sequences.
+% This approach therefore  offers sufficient flexibility for most purposes.
+% For~example, if  we now write the command \verb!\ShowSequence{,}{\rr}{\SequenceLong}!
+% we obtain
+% 
+% \medskip\noindent\verb!\ShowSequence{,}{\rr}{\SequenceLong}! \ $\longrightarrow$ \ 
+% \ShowSequence{,}{\rr}{L,R,D,D,L,L,L}
+%
+% \medskip
+%
+% In practice, any trailing digit is converted (modulo~4) and expanded accordingly, the details being
+% copied to the log-file. For~example, if one writes the command
+% \cmd{\RubikRotation\{[test],R,D28978\}}, then since $28978 \equiv 2$\,(modulo~4) then \cmd{\SequenceLong} 
+% will be returned containing the string |R,D,D|. The associated entries in the log-file  are
+% as  follows:
 %\begin{verbatim}
-% \ShowCube{3.5cm}{0.5}{\DrawNCubeAll{5}{O}{Y}{G}}
+%...rotation R OK
+%...Expanding D28978 (28978 = 2 mod 4) ...
+%...rotation D OK (= Dp3)
+%...rotation D OK (= Dp3)
+%...writing new Rubik state to file rubikstateNEW.dat
+%...SequenceName = test
+%...SequenceShort = R,D28978
+%...SequenceLong = R,D,D
 %\end{verbatim}
-%  \end{minipage}
 %
-% \medskip
 %
-%       \subsubsection[Draw.. error message]{\cmd{\draw} error message}
 %
-% See also section~\ref{sec:drawerrormessage} regarding the error message associated with 
-% using a \cmd{\Draw...} command  \textit{outside}  a TikZ picture environment.
-%  
+%  \section{SequenceBrace commands}
+%  \label{sec:sequencebrace}
+%
+%  \DescribeMacro{\SequenceBraceA} 
+%  \DescribeMacro{\SequenceBraceB} 
+%  \DescribeMacro{\SequenceBraceAF} 
+%  \DescribeMacro{\SequenceBraceBF} 
+% The  \cmd{\SequenceBraceX}\marg{name}\marg{sequence}  command 
+% is a tool for displaying a named sequence using a brace. The trailing~A 
+% denotes that the brace is placed Above the sequence; the trailing~B denotes 
+% the brace is Below the sequence.
+% Appending an `F' to the command-name (e.g.,~\cmd{\SequenceBraceAF}) results 
+% in a surrounding  fbox (cf.~the \cmd{\ShowCubeF} command). 
+% For the code see Section~\ref{sec:sequencebracecode}.
+%
+% {\noindent}Thus \verb!\SequenceBraceB{myseq}{U,D,L,R}! generates 
+% \ \SequenceBraceB{myseq}{U,D,L,R}. 
+%
+% {\noindent}A typical example of its use might be:
+%
+% \bigskip
+%
+%\noindent%
+%\RubikCubeSolved%
+%\ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}%
+%\quad\SequenceBraceA{fourspot}{\ShowSequence{}{\Rubik}{F,F,B,B,U,Dp,R,R,L,L,U,Dp}}%
+%\quad$\longrightarrow$\quad%
+%\RubikFaceFront{R}{R}{R}%
+%               {R}{O}{R}%
+%               {R}{R}{R}%
+%\RubikFaceRight{B}{B}{B}%
+%               {B}{G}{B}%
+%               {B}{B}{B}%
+%\ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}%
+%
+%
+% \bigskip
+%
+% {\noindent}which was generated by the following code, showing that the \cmd{\ShowSequence}
+% command can be used as an argument for the \cmd{\SequenceBraceA} command:
+%\begin{verbatim}
+%\newcommand{\fourspot}{[fourspot],F2,B2,U,Dp,R2,L2,U,Dp}%
+%\noindent%
+%\RubikCubeSolved%
+%\ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}%
+%\RubikRotation{\fourspot}%
+%\quad\SequenceBraceA{\SequenceName}{%
+%                     \ShowSequence{}{\Rubik}{\SequenceLong}}%
+%\quad$\longrightarrow$\quad%
+%\ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}%
+%\end{verbatim}
+% Note (1)~that the `fourspot' listing is included in the \textsc{rubikpatterns} package, and 
+% (2)~the \cmd{\RubikRotation} command requires using the \texttt{--shell-escape} command-line 
+% option  with the \LaTeX\ engine---see Section~\ref{sec:rubikrotation} for details.
+%
 %
 %
 %        \section{Arrows}
@@ -2259,31 +3092,40 @@
 %  
 %  The \rubikcube\ package does not offer any special commands for drawing 
 %  arrows since it is straightforward just to include the appropriate TikZ
-%  `draw' commands in the \texttt{tikzpicture} environment. 
+%  `draw' commands in the \texttt{tikzpicture} environment (i.e.,~in our 
+%   own \cmd{\ShowCube} environment).
 %  
-%  In order to facilitate using the standard TikZ `draw' commands both 
-%  the  RubikCubeFaceFront  and LayerFace commands have the coordinate origin 
-%  at the bottom left corner, and draw `faces' consisting of 9~unit-squares 
-%  in a  3x3 grid, as shown in  Figure~\ref{fig:facegraph}.
+%  In order to facilitate using the standard TikZ `draw' commands
+%  the  graphic grid origin of  Rubik cube images  is located at the bottom left corner 
+%  of the \textsc{front} face (see also Section~\ref{sec:coordinates} for details of the 
+%  cube's coordinate  system). Similarly,  single face images  (e.g.,~drawn using the 
+%  \cmd{\DrawFlatUp} or \cmd{\DrawFlatUpSide}  and LayerFace commands etc.)  have 
+%  their  grid origin at the bottom left corner of the face.
 %  Consequently the start and finish coordinates for any arrow or line are 
-%  easy to determine.
+%  easy to determine.  
 %  
 %  \begin{figure}[hbt]
 %     \centering
 %  \ifpdf
-%     \includegraphics[height=3cm]{Rubik-doc-figE.pdf}
+%     \includegraphics[height=3cm]{rubik-doc-figE.pdf}
 %  \else
-%  \includegraphics[height=3cm]{Rubik-doc-figE.eps}
+%  \includegraphics[height=3cm]{rubik-doc-figE.eps}
 %  \fi
-%  \vspace{-5mm}\caption{\label{fig:facegraph}RubikCubeFaceFront and RubikLayerFace coordinates} 
+%
+%  \parbox{9cm}{%
+%    \caption{\label{fig:facegraph}Grid showing the positive coordinates 
+%   associated with \textsc{front} face of a cube image, or of a face-only image.} 
+%   }%
 %  \end{figure}
 %  
-%  For example, in Figure~\ref{fig:facegraph}  we have drawn a green
-%   arrow  from the centre of cubie LB $(0.5, 0.5)$  to the centre of 
+% \medskip
+%
+%  For~example, Figure~\ref{fig:facegraph}  shows  a green
+%   arrow drawn from the centre of cubie LB $(0.5, 0.5)$  to the centre of 
 %  cubie MM\,\footnote{The code MM stands for x=Middle, y=Middle; 
 %  see also Figure~\ref{fig:facenotation} on Rubik face-notation} $(1.5, 1.5)$.
-%  To do this  we  just include  the following TikZ  command in the 
-%  \texttt{tikzpicture} environment.
+%  To do this  we  just include  the following TikZ  command, remembering that  TikZ 
+%  commands require a terminal semicolon.
 %  \begin{quote}
 %\begin{verbatim}
 %  \draw[->,color=green] (0.5,0.5) -- (1.5, 1.5);
@@ -2316,7 +3158,7 @@
 %    \draw[->,thick,color=magenta] (1.3, 2.3) -- (1.3, 0.5);
 %    \draw[<->,thick,color=magenta] (0.5,2.6) -- (2.5, 2.6);
 %    \draw[<->,thick,color=magenta] (0.5,0.3) -- (2.5, 0.3);
-%   }
+%    }
 %\end{verbatim}
 %  \end{minipage}
 %  
@@ -2357,7 +3199,7 @@
 %                          {Y}   {O}
 %     \DrawRubikLayerSideB {O}{G}{G}
 %     \draw[->,ultra thick,color=green] (0.5,5) -- (0.5, 4);
-%   }
+%     }
 %\end{verbatim}
 %  \end{minipage}
 %  
@@ -2408,39 +3250,77 @@
 %    \DrawRubikCubeRD
 %    \draw[ultra thick,->,color=blue] 
 %                (1.5,0.5) -- (2.5, 1.5);  
-%  }
+%    }
 %\end{verbatim}
 %  \end{minipage}
-%  
+%
+% \bigskip
+%
+% In the following example we use a blue circle to highlight the cubie
+% to be rotated into the top layer.
+%
+% \bigskip
+%
+% \noindent%
+% \RubikCubeGrey
+% \RubikFaceUp{X}{W}{X}%
+%             {W}{W}{W}%
+%             {W}{W}{X}%
+% \RubikSliceBottomR{X}{X}{W}{G}{X}{X}%
+% \ShowCube{2.5cm}{0.5}{%
+%   \DrawRubikCubeRU
+%   \DrawRubikLayerSideRBy{O}
+%   \draw[ultra thick,->,color=blue] (2.5,0.5) -- (2.5, 2.5);
+%   \draw [color=blue, thick] (2.7, 0.3)  circle (1.3);
+% }%
+%    \hspace{3mm}
+% \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+% \noindent%
+% \RubikCubeGrey
+% \RubikFaceUp{X}{W}{X}
+%             {W}{W}{W}
+%             {W}{W}{X}
+% \RubikSliceBottomR{X}{X}{W}{G}{X}{X}
+% \ShowCube{2.5cm}{0.5}{%
+%   \DrawRubikCubeRU
+%   \DrawRubikLayerSideRBy{O}
+%   \draw[ultra thick,->,color=blue] 
+%                              (2.5,0.5) -- (2.5, 2.5);
+%   \draw [color=blue, thick] (2.7, 0.3)  circle (1.3);
+%   }%
+%\end{verbatim}
+% \end{minipage}
 %
 %
 % \section{Final example}
 %
 % We now present, as a final example, the code used to draw the  front page 
-% figure\,\footnote{This is a sequence of order 6 used to generate the `cross' 
-% configuration when solving the cube. Doing it on  a `solved' cube allows you  
-% to see how the three edge cubies  move, and either flip (magenta arrows) or do 
-% not flip (black arrow).}. 
-% This code uses both the \rubikcube\ and  \textsc{rubikrotation} packages,
-% and therefore needs to be run using the \LaTeX\   \verb!--shell-escape! command-line switch,
-% as described in the \textsc{rubikrotation} package.
-%
+% figure\,\footnote{This is a well-known sequence of order 6 used to  cycle three
+% edge cubies; it is used to generate the `cross' configuration  in the final layer
+% when solving the cube. Here we are performing the sequence on  a `solved' cube, 
+% since this allows you  to see how the three edge cubies  move, and either 
+% flip (magenta arrows) or do not flip (black arrow).}. 
+% This code uses  the \cmd{\RubikRotation} command (from the \textsc{rubikrotation}
+%  package), and therefore the \LaTeX\ engine needs to be run using the 
+% \verb!--shell-escape!  command-line switch (see  Section~\ref{sec:rubikrotation} for details).
 %
 % \bigskip
-% \hfil
-% \RubikCubeSolved
-% \ShowCube{2cm}{0.4}{\DrawRubikCubeRU}
-% \ShowCube{2cm}{0.4}{%
+%
+% \noindent\hfil%
+% \RubikCubeSolved%
+% \ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}%
+% \quad\ShowCube{1.6cm}{0.4}{%
 %    \DrawFlatUpSide
 %    \draw[thick,->,color=magenta] (1.5,0.5) -- (2.4, 1.4);
 %    \draw[thick,->] (2.5,1.5) -- (1.6, 2.4);
 %    \draw[thick,->,color=magenta] (1.3, 2.3) -- (1.3, 0.5);
 %    \draw[thick,<->,  color=blue] (0.5,2.6) -- (2.5, 2.6);
 %    \draw[thick,<->,  color=blue] (0.5,0.3) -- (2.5, 0.3);
-% }
-% \Rubik{F}\Rubik{R}\Rubik{U}\Rubik{Rp}\Rubik{Up}\Rubik{Fp}%
-% \ \ \ $\longrightarrow$
-% \ShowCube{2cm}{0.4}{%
+%   }%
+% \quad\Rubik{F}\Rubik{R}\Rubik{U}\Rubik{Rp}\Rubik{Up}\Rubik{Fp}%
+%  \quad$\longrightarrow$%
+%  \quad\ShowCube{1.6cm}{0.4}{%
 %     \DrawRubikLayerFace{W}{W}{B}
 %                        {W}{W}{O}
 %                        {W}{R}{B}
@@ -2451,31 +3331,30 @@
 %     \DrawRubikLayerSideB {G}{W}{O}
 % }
 % \hfil
-% \bigskip
 %
+% \bigskip
 %
 %\begin{verbatim}
-% \hfil
-% \RubikCubeSolved
-% \ShowCube{2cm}{0.4}{\DrawRubikCubeRU}
-% \ShowCube{2cm}{0.4}{%
-%    \DrawFlatUpSide
+% \noindent\hfil%
+% \RubikCubeSolved%
+% \ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}%
+% \quad\ShowCube{1.6cm}{0.4}{%
+%    \DrawFlatUpSide%
 %    \draw[thick,->,color=magenta] (1.5,0.5) -- (2.4, 1.4);
 %    \draw[thick,->] (2.5,1.5) -- (1.6, 2.4);
 %    \draw[thick,->,color=magenta] (1.3, 2.3) -- (1.3, 0.5);
 %    \draw[thick,<->,  color=blue] (0.5,2.6) -- (2.5, 2.6);
 %    \draw[thick,<->,  color=blue] (0.5,0.3) -- (2.5, 0.3);
-% }
-% \Rubik{F}\Rubik{R}\Rubik{U}\Rubik{Rp}\Rubik{Up}\Rubik{Fp}%
-% \ \ \ $\longrightarrow$
-% \RubikRotation{F,R,U,Rp,Up,Fp}
-% \ShowCubeF{2cm}{0.4}{\DrawFlatUpSide}
+%    }%
+% \RubikRotation{F,R,U,Rp,Up,Fp}%
+% \quad\ShowSequence{}{\Rubik}{\SequenceLong}\quad$\longrightarrow$%
+% \ShowCube{1.6cm}{0.4}{\DrawFlatUpSide}%
 % \hfil
 %\end{verbatim}
 %
 %
 %
-%     \subsection[Without using {\textbackslash}RubikRotation]{Without using \cmd{\RubikRotation..}}
+%     \subsection[Without using {\textbackslash}RubikRotation]{Without using \cmd{\RubikRotation}}
 %
 % If you really need to draw the above figure \textit{without}  using 
 % the \textsc{rubikrotation}  package (as we had to in order to write 
@@ -2483,11 +3362,14 @@
 % commands
 %\begin{verbatim}
 % \RubikRotation{F,R,U,Rp,Up,Fp}
-% \ShowCubeF{2cm}{0.4}{\DrawFlatUpSide}
+% \ShowSequence{,}{\Rubik}{\SequenceLong} \ \ \ $\longrightarrow$
+% \ShowCube{2cm}{0.4}{\DrawFlatUpSide}
 %\end{verbatim}
-% with the following set of \cmd{\DrawRubikLayer...} commands.
+% with the following commands:
 %
 %\begin{verbatim}
+% \Rubik{F}\Rubik{R}\Rubik{U}\Rubik{Rp}\Rubik{Up}\Rubik{Fp}
+% \ \ \ $\longrightarrow$
 % \ShowCube{2cm}{0.4}{%
 %     \DrawRubikLayerFace{W}{W}{B}
 %                        {W}{W}{O}
@@ -2497,71 +3379,129 @@
 %                          {B}   {W}
 %                          {O}   {W}
 %     \DrawRubikLayerSideB {G}{W}{O}
-% }
+%     }
 %\end{verbatim}
 %
 %
 %
 %
 %
-%  \section{Known issues \& shortcomings}
+%  \section{Known limitations}
 %
-% Please contact the authors regarding any ideas, errors or shortcomings etc. 
+% Please contact the authors regarding any ideas for improvement, errors, 
+% problems or shortcomings etc. 
 %
 % \begin{itemize} 
 %  
-%  \item  The rotation hieroglyphs are optimised for a 10pt font, and  do 
-%    not  scale  with document  font size.  However, they do 
-%   seem to  work reasonably well with both 11pt and 12pt fonts.
-%  Any suggestions are welcome.
-%
-%  \item The sidebars cannot be arbitrarily positioned.
+%  \item  Note that  the rotation hieroglyphs are optimised for a 10pt font
+%  and  do  not  scale  with document  font size. However, they do work well  in 
+%  conjunction with the standard 11pt and 12pt document fonts sizes. Nevertheless, 
+%  the font size can of course be changed by renewing the font command 
+%  (see Section~\ref{sec:rubikfont} for details).
+%
+%  \item The sidebars cannot be arbitrarily positioned (note: hidden 
+%  faces can be arbitrarily positioned).
 % 
 % \end{itemize}
 %
 %
-%  \section{Acknowledgements}
-%  
-%  We would like to thank Peter Bartal and  Peter Grill for useful ideas and  
-%  suggestions.   We have built on some of their ideas and have acknowledged
-%  these instances in the documentation. 
-%  We would also like to  thank Christian Tellechea for the  \cmd{\@join\{\}\{\}} command.
-%  
-%
-%
-%   \section{Future supporting packages}
+%   \section{Future packages}
 %  
 %  Since  Rubik-type cubes currently exist in  a variety of sizes (from 2x2x2 to 11x11x11)
-%  it is possible that similar packages dealing with cubes of other sizes may be made in 
-%  the future.  Supporting tools  may also be  made
+%  other authors may well create  similar packages dealing with 
+%  cubes of other sizes the future.  Supporting tools  may also be  made
 %  using various programming languages, e.g.,~Lua etc. Consequently  the naming of such 
 %  packages and tools, and even the associated CTAN directories, needs to be given 
 %  some thought in order to prevent possible confusion.
 %
-%  In the event of new  packages being made, we suggest that a CTAN directory structure 
+%  In the event of new  packages being made, may we suggest that a CTAN directory structure 
 %  along the following lines might be  appropriate.
 %  
 %  $$
-%  \textsc{rubik}  \left\{
-%    \begin{array}{l} 
-%    \mbox{rubiktools}\\
-%    \mbox{rubik2x}\\
-%    \mbox{rubik3x}\\
-%    \ldots\\
-%    \mbox{rubik11x}\\
-%    \end{array}
-%         \right.\\
+%  \textsc{rubik}  
+%    \left\{
+%      \begin{array}{l} 
+%      \mbox{rubiktools}\\
+%      \mbox{rubik2x}\\
+%      \mbox{rubik3x}\\
+%      \ldots\\
+%      \mbox{rubik11x}\\
+%      \end{array}
+%    \right.\\
 %  $$
 %
 %
 % 
-%     \section{History}
+%     \section{Change history}
 %
 % \begin{itemize}
-
+%
+% \item Version 4.0 (March 2017)
+%
+%  ---Improved documentation.
+%
+%  ---Improved inter-hieroglyph spacing and vertical position. The Computer Moderm sans bold font
+%     (10/12pt) is used for the hieroglyphs and rotation codes (see Section~\ref{sec:coderubikfont}
+%     for details).
+%
+%  ---Improved the \cmd{\ShowCube} and \cmd{\ShowCubeF} macros (see Sections~\ref{sec:showcube}
+%   and \ref{sec:showcubecode}).
+%
+%  ---Additional notation for middle slice rotations (`m' notation), e.g.,~\rr{Rm}, \rr{Rmp} etc 
+%  (see Sections~\ref{sec:mnotation} and \ref{sec:codeJaap}).
+% 
+%  ---Additional notation for whole cube rotations (`c' notation),  e.g.,~\rr{Rc}, \rr{Rcp} etc 
+%  (see Sections~\ref{sec:cnotation} and \ref{sec:codeJaap}).
+%
+%  ---Added Randelshofer notation  (the `CMST' rotations),  e.g.,~\rr{CR}, \rr{MR} etc 
+%  (see Sections~\ref{sec:listofRandelshofercommands} and \ref{sec:codeRandelshofer}).
+%
+%  
+%  ---Two new (more-intuitive) \cmd{\Draw..} commands replace earlier (now deprecated) 
+% ambiguous versions; these new versions are now consistent with 
+%  the other  \cmd{\DrawRubikCubeXX} commands (see Section~\ref{sec:flatcommands}).
+% \begin{quote}
+% \cmd{\DrawRubikCubeF} (F = flat) ---replaces  \cmd{\DrawRubikFlat}. 
+% \newline\cmd{\DrawRubikCubeSF} (SF = semi-flat) ---replaces \cmd{\DrawRubikCubeFlat}.
+% \end{quote}
+%
+%
+%  ---Six new commands for showing  and annotating rotation sequences; the versions with a 
+% terminal `F' also surround the object with an fbox to allow users to see the extent
+% of any associated white space 
+% (see Sections~\ref{sec:showsequence} \&  \ref{sec:sequencebrace}):
+% \begin{quote}
+% \cmd{\ShowSequence}
+% \newline\cmd{\ShowSequenceF}
+% \newline\cmd{\ShowSequencef}
+% \newline\cmd{\SequenceBraceA}
+% \newline\cmd{\SequenceBraceAF}
+% \newline\cmd{\SequenceBraceB}
+% \newline\cmd{\SequenceBraceBF}
+%
+% \end{quote}
+%
+%  ---A new command for setting up  or allocating a `solved'  colour configuration.
+%  (see Section~\ref{sec:solvedconfig}):
+% \begin{quote}
+% \cmd{\SolvedConfig}
+% \end{quote}
+%
+%  ---A new command for setting up a `starter cube' for which the \textit{whole} cube  
+% is allocated the default `grey' colour  (see Section~\ref{sec:rubikcubegrey}):
+% \begin{quote}
+% \cmd{\RubikCubeGreyAll}
+% \end{quote}
+%
+%  ---A new supporting \textsc{rubikpatterns} package has been added to
+%   the  Rubik bundle. It is a small macro database of well-known  named  Rubik patterns 
+%   and associated sequences (see Section~\ref{sec:patterns}).
+%
+%
+%
 % \item Version 3.0 (September 2015)
 %
-%  ---All rotation commands can now use the rotation-code as an argument; for example, 
+%  ---All rotation commands can now use the rotation-code as an argument; for~example, 
 % the rotation \rr{D} can now be typeset using the command \cmd{\rr\{D\}} etc 
 %  (see Section~\ref{sec:RubikCommands}).
 % The new rotation commands are:
@@ -2605,13 +3545,13 @@
 %
 % ---Changed `Equator' $\rightarrow$ `Middle' in  all \cmd{\DrawLayer..} 
 % commands (for consistency). Hence `E' $\rightarrow$ `M' in all Flat 
-% commands and Slice commands. Note although former  use of `Equator' is
+% commands and Slice commands. Note that although the former  use of `Equator' is
 % retained for backward compatibility (for the moment) it is now deprecated. 
 %
 % ---Fixed a conflict with the \TeX\ \cmd{\sb} command as used by the  \textbf{url} 
 % package which resulted in  reference chaos when the \textbf{url} package was used with 
-% the \Rubikcube\ package (internalised \cmd{\sb} to \cmd{\@sb}). Also  internalised for 
-%  convenience  \cmd{\sd} to \cmd{\@sd}; \cmd{\sh} to \cmd{\@sh}; \cmd{\sc} to \cmd{\@sc};
+% the \Rubikcube\ package (internalised \cmd{\sb} to \cmd{\@sb}). Also  internalised, for 
+%  convenience,  \cmd{\sd} to \cmd{\@sd}; \cmd{\sh} to \cmd{\@sh}; \cmd{\sc} to \cmd{\@sc};
 % \cmd{\sq} to \cmd{\@sq}.
 % 
 %
@@ -2623,13 +3563,25 @@
 %
 %
 %
+%  \section{Acknowledgements}
+%  
+%  We would like to thank Peter Bartal and  Peter Grill for useful ideas and  
+%  suggestions.   We have built on some of their ideas and have acknowledged
+%  these instances in the documentation. 
+%  Finally, we would like to  thank Christian Tellechea for the  \cmd{\@join\{\}\{\}} 
+%  command  (see Section~\ref{sec:usefulinternalcommands}), 
+%  Christian Schr\"{o}ppel for help regarding the \textsf{forarray} package 
+%  (see Section~\ref{sec:codeshowsequence}), and  Herbert Kociemba for helpful comments.
+%  
+%
+%
+%
 %    \section{References}
 %  
 %  \begin{itemize}
 %  
 %  
-%  \item  Bartal P (2011)
-%  
+%  \item  Bartal P (2011). \ 
 %  \url{http://tex.stackexchange.com/questions/34482/}
 %  
 %  \item Chen JJ (2004). Group theory and the Rubik's cube.
@@ -2638,7 +3590,7 @@
 %
 % \item Davis T (2006). Group theory via Rubik's cube. 
 %  \url{http://www.geometer.org/rubik/group.pdf}
-  
+%  
 %  \item Demaine ED, Demaine ML, Eisenstat S, Lubiw A and Winslow A (2011).
 %  Algorithms for solving Rubik's cubes.
 %  \url{http://www.arxiv.org/abs/1106.5736/}
@@ -2658,14 +3610,16 @@
 %  \newline\url{http://duvoid.fr/rubik/rubik-friddrich-couleurs.pdf}
 %  \newline\url{http://duvoid.fr/rubik/sources/rubik-friddrich-couleurs.tex}
 %
-% \item Feuers\"{a}nger (2015). Manual for package \textsc{pgfplots} 
-% (\texttt{pgfplots.pdf}).  v\,1.12.1 (2015/05/02),  \S\,3.2.3, page~20.
-%  \url{http://www.ctan.org/pkg/pgfplots}.
+% \item Feuers\"{a}nger (2016). Manual for package \textsc{pgfplots}. 
+% v\,1.13 (2016/01/06),  \S\,3.2.3, page~21. (\texttt{pgfplots.pdf})
+%  \url{http://www.ctan.org/pkg/pgfplots}. [re: preventing extra white space]
 %  
-%  \item Fridrich J. \ \  \url{http://www.ws.binghamton.edu/fridrich/}.  
+%  \item Fridrich website (Fridrich J.) \ \  \url{http://www.ws.binghamton.edu/fridrich/}.  
 %  See the useful `notation' section  on the `Pretty patterns' webpage at 
 %  \url{http://www.ws.binghamton.edu/fridrich/ptrns.html}.
 %
+%  \item Frey AH and Singmaster D (1982). \textit{Handbook of cubik math}, 
+%  (Enslow Publishers, Inc.) (republished: 2010, Lutterworth Press, UK)
 %
 %  \item Golomb SW (1981). Rubik's cube and a model of quark confinement.
 %  \textit{Am.\ J.\ Phys.}; vol~49, pp~1030--1031. 
@@ -2678,12 +3632,13 @@
 %  \item Gymrek M (2009). The mathematics of the Rubik's cube.
 %  \newline\url{http://web.mit.edu/sp.268/www/rubik.pdf}
 %  
+%  \item Heise website (Heise R). Rubik's cube theory. \url{http://www.ryanheise.com/cube/theory.html}
+%
 %  \item Hofstadter D (1981). Rubik cube. \textit{Scientific American}; March issue.
 %  
 %  \item Hutchings M (2011). The mathematics of Rubik's cube (slide presentation). 
 %        \url{http://math.berkeley.edu/~hutching/rubik.pdf}
 %
-%
 % \item Jelinek website (Jelinek J). Rubik's cube solution methods.
 %  \url{http://www.rubikscube.info/}    
 %  
@@ -2691,18 +3646,29 @@
 %       Rubik's cube, Merlin's machine and other mathematical toys}; pp~322.
 %  \url{http://www.mike.verdone.ca/media/rubiks.pdf}
 %  
-%  \item Kociemba  website (Kociemba H). \url{http://www.kociemba.org/cube.htm}
-%  
+% 
+% \item  Kociemba website (Kociemba H).  \url{http://www.kociemba.org/cube.htm}
+% {\newline}---for superflip see: \url{http://www.kociemba.org/math/oh.htm}
+%
+%
 %  \item Kriz I and Siegel P (2008). Rubik's cube-inspired puzzles demonstrate math's 
 % simple groups.  \textit{Scientific American};  July 2008 
 %  
+%  \item Longridge website (Longridge M).  The cube pattern archive. \url{http://www.cubeman.org}
 %
 %  \item Randelshofer website (Randelshofer W).  Pretty patterns. 
 %  \url{http://www.randelshofer.ch/rubik/patterns/}
 %
-%   \item Reid website (Reid M) \ \  \url{http://www.cflmath.com/Rubik/}, 
+%   \item Reid website (Reid M) \ \  \url{http://www.cflmath.com/Rubik}, 
 %       for patterns see \url{http://www.cflmath.com/Rubik/patterns.html}
 %
+% \item Reid M. (1995). Superflip requires 20 face turns. (January 1995) 
+%   \url{http://www.math.ucf.edu/~reid/Rubik/CubeLovers/}  
+% {\newline}[cited from Rokicki \textit{et~al.}, 2013]. 
+% {\newline}(Note: easier to use is the following html indexed version of the 
+% archive of the Cube-Lovers usenet group (1982--1997)  
+% \url{http://www.math.rwth-aachen.de/~Martin.Schoenert/Cube-Lovers/})
+%
 %  
 %  \item Rokicki T, Kociemba H, Davidson M and Dethridge J (2013). The diameter of the 
 %       Rubik's cube is twenty.  \textit{SIAM.\ J.\ Discrete Math.}, \underline{27}, 1082--1105.
@@ -2711,7 +3677,15 @@
 %  \item Rubik's cube. See Section on notation. 
 %  \newline\url{http://en.wikipedia.org/wiki/Rubik's_Cube}
 %  
-%  \item Speedsolving website. \url{www.speedsolving.com/}
+%  \item RuWix website (Ferenec D) \ \ \url{http://www.ruwix.com}.
+%  See the online Rubik's cube solver  \url{http://www.ruwix.com/online-rubiks-cube-solver-program}.
+%
+%  \item Scherphius  website (Scherphius J).  Jaap Puzzles website 
+%       \url{http://www.jaapsch.net/puzzles/symmetr1.htm} 
+%
+% \item Singmaster D (1981). \textit{Notes on Rubik's magic cube} (Harmondsworth, Eng., Penguin Books)
+%
+%  \item Speedsolving website. \url{http://www.speedsolving.com/}
 %  
 %  \item Tran R (2005). A mathematical approach to solving Rubik's cube.
 %  \url{http://www.math.ubc.ca/~cass/courses/m308/projects/rtran/rtran.pdf}
@@ -2722,9 +3696,9 @@
 %    [cited from \textit{Wikipedia} (Rubik's cube)]
 %
 %  
-%  \item Vandenbergh L. \ \ \textsc{cubezone} \url{http://www.cubezone.be}
+%  \item Vandenbergh website (Vandenbergh L.) \ \ \textsc{cubezone} \url{http://www.cubezone.be}
 %  
-%  \item WCA (2015). World Cube Association Regulations. See Section~12 for notation.
+%  \item WCA (2016). World Cube Association Regulations. See \S\,12 for notation.
 %   \url{http://www.worldcubeassociation.org/regulations.htm}
 %  
 %  
@@ -2742,17 +3716,17 @@
 %  The conventions  we adopt regarding  capital letters and the 
 %  XYZ argument ordering are detailed in  Section~\ref{sec:conventions}.
 %
-% Note that it is  important in a graphics package to use a trailing \% on 
-% the end of lines which  break  before the terminal curley bracket of a newcommand.
+% Note that it is  important when using a graphics package to use a trailing \% on 
+% the end of lines which  break  before the terminal curly bracket of a \cmd{\newcommand}.
 % This is to prevent accumulating spurious spaces which may otherwise appear in 
-% figures and diagrams as a strange or unexpected horizontal shift or whitespace.
+% figures and diagrams as a strange or unexpected horizontal shift or white-space.
 %
 %   \subsection{\hspace{3mm}Package heading}
 %
 %    \begin{macrocode}
 %<*rubikcube>
-\def\RCfileversion{3.0}%
-\def\RCfiledate{2015/09/25}%
+\def\RCfileversion{4.0}%
+\def\RCfiledate{2017/03/03}%
 \NeedsTeXFormat{LaTeX2e}
 \ProvidesPackage{rubikcube}[\RCfiledate\space (v\RCfileversion)]
 %    \end{macrocode}
@@ -2763,100 +3737,38 @@
   \RequirePackage{tikz}}%
 %    \end{macrocode}
 %
-%    \begin{macro}{\rubikcube}
-%  First we create a suitable logo
+%  The package requires the Forarray package (see Section~\ref{sec:codeshowsequence})---so 
+%  we load it if not already loaded.
 %    \begin{macrocode}
-\newcommand{\rubikcube}{\textsc{rubikcube}}%
-\newcommand{\Rubikcube}{\textsc{Rubikcube}}%
+\@ifpackageloaded{forarray}{}{%
+  \typeout{---rubikcube requires the Forarray package.}%
+  \RequirePackage{forarray}}%
 %    \end{macrocode}
-%    \end{macro}
-%
-%
-%   \subsection{\hspace{3mm}Some useful internal commands}
-%  \label{sec:usefulinternalcommands}
-%
-%  \begin{macro}{\@rr} 
-%  \begin{macro}{\@rrp}
-%  \begin{macro}{\@rrw} 
-%  \begin{macro}{\@rrwp} 
-%  \begin{macro}{\@rrs} 
-%  \begin{macro}{\@rrsp}
-%  \begin{macro}{\@rra} 
-%  \begin{macro}{\@rrap} 
-%  \begin{macro}{\@xyzh} 
-%  \begin{macro}{\@xyzhp} 
-%  \begin{macro}{\@xyzRubik} 
-%  \begin{macro}{\@xyzRubikp} 
-%  \begin{macro}{\@SquareLetter} 
-%  \begin{macro}{\@hRubik} 
-% Internal commands. These  are used to generate the
-% prime, w, w-prime, s, s-prime, a, a-prime   
-% rotation commands. The \cmd{\@xyz..} commands are used to generate the 
-% x,y,z,u,d,l,r,f,b, and their prime rotation commands.
-% The \cmd{\@SquareLetter} command is used to form the separate square hieroglyph  form
-% used for rotations with no visible representation from the front 
-% (eg~B.., Fs, Fsp, Fa, Fap, S, Sp, Sf, Sfp, Sb, Sbp).
-% The \cmd{\@hRubik} is the vertical shift  used  to raise the box carying the rotation 
-% rotation-code in \cmd{\Rubik..} commands not visible from the front.
 %
-%  The idea is that by using these internal
-% tools we will be able to more easily standardise the  size and position 
-% of all the various glyphs. However, these internal tools are currently 
-% only partially implemented (= work in progress).
-% \begin{macrocode}
-\newcommand{\@rr}[1]{\textbf{\textsf{#1}}}
-\newcommand{\@rrp}[1]{\textbf{\textsf{#1}$^\prime$}}
-\newcommand{\@rrw}[1]{\textbf{\textsf{#1\footnotesize{w}}}}
-\newcommand{\@rrwp}[1]{\textbf{\textsf{#1\footnotesize{w}}$^\prime$}}
-\newcommand{\@rrs}[1]{\textbf{\textsf{#1\footnotesize{s}}}}
-\newcommand{\@rrsp}[1]{\textbf{\textsf{#1\footnotesize{s}}$^\prime$}}
-\newcommand{\@rra}[1]{\textbf{\textsf{#1\footnotesize{a}}}}
-\newcommand{\@rrap}[1]{\textbf{\textsf{#1\footnotesize{a}}$^\prime$}}
-\newcommand{\@xyzh}[1]{\textbf{[\textsf{#1}]}\,}
-\newcommand{\@xyzhp}[1]{\textbf{[\textsf{#1}$^\prime$]}\,}
-\newcommand{\@xyzRubik}[1]{\raisebox{3.45pt}{\textbf{[\textsf{#1}]}}}
-\newcommand{\@xyzRubikp}[1]{\raisebox{3.45pt}{\textbf{[\textsf{#1}$^\prime$]}}}
-\newcommand{\@SquareLetter}[1]{\setlength\fboxsep{2.5pt}\fboxrule=0.8pt%
-   \fbox{\rule[-1pt]{0pt}{8.5pt}\raisebox{-0.5pt}{#1}}}
-\newlength\@hRubik%
-\setlength{\@hRubik}{0.185cm}%
+%  The package requires the IfThen package (see Section~\ref{sec:codeshowsequence})---so 
+%  we load it if not already loaded.
+%    \begin{macrocode}
+\@ifpackageloaded{ifthen}{}{%
+  \typeout{---rubikcube requires the IfThen package.}%
+  \RequirePackage{ifthen}}%
 %    \end{macrocode}
-%  \end{macro}
-%  \end{macro}
-%  \end{macro}
-%  \end{macro}
-%  \end{macro}
-%  \end{macro}
-%  \end{macro}
-%  \end{macro}
-%  \end{macro}
-%  \end{macro}
-%  \end{macro}
-%  \end{macro}
-%  \end{macro}
-%  \end{macro}
 %
 %
-%  \begin{macro}{\@join} 
-%  We also require a macro for joining two strings  so we can convert
-%  a rotation-code, say U,  into a macro which typesets it in some form, say \cmd{\rrhU}.
-%  The following \cmd{\@join\{\}\{\}} command is by Christian Tellechea.
-%  {\newline}Usage: \cmd{\@join\marg{command-stem}\marg{rotation-code}}. For example, 
-%  to create the command \cmd{\rrhU} we would write |\@join{\rrh}{U}|, and hence 
-%  the command |\rrh{U}| is equivalent to \cmd{\rrhU} (see Section~\ref{sec:cmdsusingjoin}).
-%  {\newline}Since this macro is also useful for processing rotation-codes in a  list, 
-%  which may also include macros, it is important that |#2| is not detokenized.
-% \begin{macrocode}
-\newcommand*\@join[2]{%
-    \csname\expandafter\@gobble\string#1#2\endcsname}
+%
+%    \begin{macro}{\rubikcube}
+%  First we create a suitable logo
+%    \begin{macrocode}
+\newcommand{\rubikcube}{\textsc{rubikcube}}%
+\newcommand{\Rubikcube}{\textsc{Rubikcube}}%
 %    \end{macrocode}
-%  \end{macro}
+%    \end{macro}
 %
 %
 %   \subsection{\hspace{3mm}Colours}
 %  \label{sec:codecolours}
 %
-%  These colour allocations were initially defined by Peter Bartal (2011).
+%   We have adopted the following colour allocations; these  were initially 
+%  defined by Peter Bartal (2011) ---see Section~\ref{sec:colours}.
 %  We have modified only the colour grey, which is now defined as {black!30}.
 %
 %    \begin{macrocode}
@@ -2871,6 +3783,37 @@
 %
 %
 %
+%   \subsection{\hspace{3mm}The rubikfont}
+%  \label{sec:coderubikfont}
+%
+%  \begin{macro}{\@rubikfont} 
+%  \begin{macro}{\@rubikfontFNS}
+%  \begin{macro}{\@rubikprime}
+% We define two  fonts for text associated with the Rubik glyphs 
+% (both the `arrow' glyphs and the `letter' glyphs), 
+% namely, (1)~Computer Modern Sans (cmss), bold extended (bx), normal shape (n) 
+% at 10/12pt, and  (2)~a footnotesize (FNS) version (8pt) for the lower-case letters  
+% [for cmss see Latex Companion (2004), p.\,417 \& p.\,354\,\footnote{Note the typo in Table~7.5 (p.\,354): 
+% the  font-series code for the Sans semi-bold condensed  form is `sbx' (not sbc).}]. 
+% This has the effect of  keeping the size
+% of Rubik glyphs constant in the face of any changes in the document fonts.
+% We make the baseline-skip values the same, since the `arrow' glyphs generated by 
+% the  \cmd{\Rubik} commands involve  a single baseline-skip (for example, as with 
+% \verb!\Rubik{D}!; see Section~\ref{sec:coderotationD}). 
+% We  use the cmss font  apostrophe as the  `prime' symbol (the user has 
+% the opportunity to use the maths \cmd{\prime} 
+% instead---see Section~\ref{sec:rubikprime}). 
+%\begin{macrocode}
+\newcommand{\@rubikfont}{\fontsize{10}{12pt}\usefont{T1}{cmss}{bx}{n}} 
+\newcommand{\@rubikfontFNS}{\fontsize{8}{12pt}\usefont{T1}{cmss}{bx}{n}} 
+\newcommand{\@rubikprime}{'}
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%
+%
+%
 %  \subsection{\hspace{3mm}ShowCube command}
 %  \label{sec:showcubecode}
 %
@@ -2880,42 +3823,181 @@
 %  displays the cube inside a minipage, so that we can easily tailor the minipage 
 %  width (|#1|) and also the  TikZ scale factor (|#2|). The \cmd{\ShowCubeF} command
 %  places an fbox around the minipage so users can see the extent of any white space.
-% {\newline}\textsc{usage}: |\ShowCube{2cm}{0.5}{\DrawRubikCubeRU}|
+%  {\newline}\textsc{usage}: |\ShowCube{2cm}{0.5}{\DrawRubikCubeRU}|
+%
+% February 2017 (RWDN): \ We first require a new length variable (which will become the minipage-width),
+% so we can add the length 1.6pt to it (this is the width of the TikZ ultra-thick line
+% which is used to draw the Rubik cubes). 
+% In order for a width of an image made up of $x$~units to be equal 
+% to $x \times (\mbox{scale-factor})$ we need to add an extra line-width 
+% (i.e.,~to include the right-hand edge). 
+%    \begin{macrocode}
+\newlength{\@showcubewidth}% 
+%    \end{macrocode}
+% We can now build the two macros. We set the \cmd{\fboxsep} value to zero.
 %    \begin{macrocode}
 \newcommand{\ShowCube}[3]{%
-  \begin{minipage}{#1}%
+  \setlength{\fboxsep}{0cm}% 
+  \setlength{\@showcubewidth}{#1}%
+  \advance\@showcubewidth by 1.6pt\relax% 
+  \begin{minipage}{\the\@showcubewidth}%
   \centering%
   \begin{tikzpicture}[scale=#2]%
   #3%
   \end{tikzpicture}%
   \end{minipage}%
-}
+}%
 \newcommand{\ShowCubeF}[3]{%
-  \fbox{%
-  \begin{minipage}{#1}%
+  \setlength{\fboxsep}{0cm}% 
+  \setlength{\fboxrule}{0.4pt}% 
+  \setlength{\@showcubewidth}{#1}%
+  \advance\@showcubewidth by 1.6pt\relax% 
+  \framebox{%
+  \begin{minipage}{\the\@showcubewidth}%
   \centering%
   \begin{tikzpicture}[scale=#2]%
   #3%
   \end{tikzpicture}%
   \end{minipage}%
-}}
+}}%
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
+%
+%
+%
+%
+%  \subsection{\hspace{3mm}ShowSequence command}
+%  \label{sec:codeshowsequence}
+%
+%  \begin{macro}{\ShowSequence} 
+%  \begin{macro}{\ShowSequenceF} 
+%  \begin{macro}{\ShowSequencef} 
+% The  \cmd{\ShowSequence}\marg{separator}\marg{font-code}\marg{sequence}  command 
+% typesets a comma separated sequence of rotation commands. 
+% (See Section~\ref{sec:showsequence}).
+% This command takes three mandatory arguments: the first is the separator  (\verb!#1!), 
+% the second is  the font or style code (\verb!#2!), and third is a comma-separated 
+% sequence of Rubik  rotation commands (|#3|).
+%
+%  This command requires the \texttt{forarray} 
+%  package---by Christian Schr\"{o}ppel---(for the \cmd{\ForEachX} command)
+%  and the \texttt{ifthen} package---by David Carlisle---(for the \cmd{\ifthenelse} command).
+%  These two packages are loaded at startup if not already loaded.
+%  We first need to define two variables  for use by the command; these are
+%  derived from the \texttt{forarray} package.
+%
+%    \begin{macrocode}
+\newcommand{\x}{\thislevelitem}
+\newcommand{\xcount}{\thislevelcount}
+%    \end{macrocode}
+%
+%  The \cmd{\ShowSequence} command typesets a sequence of elements, and places 
+%  an optional separator (|#1|) between them.
+%  For each element of |#3| this command  forms the construction |#2{element of #3}|.
+%  For~example, if |#2 = \rr|,  and an element of |#3| is D, then it forms |\rr{D}| etc.
+%
+%  Note that in order to avoid placing a trailing comma after the final element,
+%  we identify the first element (using |\xcount|) and then place a  comma in front 
+%  all the remaining elements. This is because it is easy to identify the first element
+%  of a sequence, but very difficult to identify the final element.
+%
+%  We also create two fbox forms: the `F' form places an fbox about the whole output; 
+% the `f' form places an fbox about each element in the output (these forms can be 
+% helpful when checking white space.
+%
+%  \noindent\textsc{usage}:  |\ShowSequence{,}{\rr}{R,L,Up,Dp.....}|
+%
+%    \begin{macrocode}
+\newcommand{\ShowSequence}[3]{%
+   \ForEachX{,}{%
+    \ifthenelse{\xcount=1}{#2{\x}}{#1#2{\x}}%
+    }{#3}%
+}%
+\newcommand{\ShowSequenceF}[3]{%
+\fbox{%
+   \ForEachX{,}{%
+    \ifthenelse{\xcount=1}{#2{\x}}{#1#2{\x}}%
+    }{#3}%
+}}%
+\newcommand{\ShowSequencef}[3]{%
+   \ForEachX{,}{%
+    \ifthenelse{\xcount=1}{\fbox{#2{\x}}}{#1{\fbox{#2{\x}}}}%
+    }{#3}%
+}%
 %    \end{macrocode}
+%  \begin{macro}{\SequenceInfo} 
+%  \begin{macro}{\SequenceName} 
+%  \begin{macro}{\SequenceShort} 
+%  \begin{macro}{\SequenceLong} 
+%  \noindent\textsc{Sequence holders}:  providing none of the Rubik rotation-codes  has  a trailing
+%   integer (e.g.,~R3) then  the Rubik macros (|\rr|, |\rrh|, |\Rubik|, |\textRubik|) will work 
+%   as expected when used as the second argument in the \cmd{\ShowSequence} command
+%   (described above). However, a problem arises when trying to process in this way any Rubik
+%   rotation-codes having a terminal integer (for example, short-codes e.g.,~R2, D3,...), since the 
+%  \cmd{\ShowSequence} macro cannot expand  short-codes into  their long-code 
+%  elements (e.g.,~~R,R,D,D,D,...). 
+%
+%   Accommodating such codes  when using the \cmd{\ShowSequence} command is currently 
+%   solved by using separate  `holders' for  four derived strings, namely: \cmd{\SequenceInfo},
+%   \cmd{\SequenceName},\cmd{\SequenceShort} and \cmd{\SequenceLong} 
+%   (for details see Section~\ref{sec:showsequence}).
+%   These  are generated automatically by  the Perl  \textsc{rubikrotation} program, which returns
+%   a so-called `long' version of the `short' string (the argument of the \cmd{\RubikRotation}
+%   command).  For~example, the Perl program converts 
+%   any short codes  (e.g.,~R2, D3,... ) $\rightarrow$ long form, e.g.,~R,R,D,D,D,... 
+%   (see the \textsc{rubikrotation} documentation for details).
+%   In order for the four `holders' of these  derived strings generated by the Perl program
+%   (written to the file \texttt{rubikstateNEW.dat}) to be accessible to  the user they need to
+%   defined  here so that they can then be `redefined' (by the Perl program) in the file
+%    \texttt{rubikstateNEW.dat}: 
+%    \begin{macrocode}
+\newcommand{\SequenceInfo}{{}}%   %% INFO only
+\newcommand{\SequenceName}{{}}%   %% NAME only
+\newcommand{\SequenceShort}{{}}%  %% original SHORT seq but with NO NAME   
+\newcommand{\SequenceLong}{{}}%   %% just the LONG string \& no name 
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
 %  \end{macro}
 %  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%
+%
+%
+%  \subsection{\hspace{3mm}SequenceBrace commands}
+%  \label{sec:sequencebracecode}
 %
+%  \begin{macro}{\SequenceBraceA} 
+%  \begin{macro}{\SequenceBraceB} 
+% The  \cmd{\SequenceBraceX}\marg{name}\marg{sequence}  command 
+% is a tool for displaying a named sequence using a brace. The trailing~A 
+% denotes that the brace is placed Above the sequence; B~denotes the brace is Below the sequence.
+% For usage see Section~\ref{sec:sequencebrace}.
+%
+%    \begin{macrocode}
+\newcommand{\SequenceBraceA}[2]{$\overbrace{\mbox{#2}}^{\mbox{#1}}$}%
+\newcommand{\SequenceBraceB}[2]{$\underbrace{\mbox{#2}}_{\mbox{#1}}$}%
+\newcommand{\SequenceBraceAF}[2]{\fbox{$\overbrace{\mbox{#2}}^{\mbox{#1}}$}}%
+\newcommand{\SequenceBraceBF}[2]{\fbox{$\underbrace{\mbox{#2}}_{\mbox{#1}}$}}%
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
 %
 %
 %  \subsection{\hspace{3mm}Face commands}
 %
-% Cube face notation = U, D, L, R, F, B (Singmaster)
-% {\newline}Cubie-square notation = t, m, b, l, m, r = top, middle, 
+% Cube face notation: U, D, L, R, F, B (Singmaster)
+% {\newline}Cubie-square notation:  t, m, b, l, m, r = top, middle, 
 % bottom, left, middle, right.
-% We  use t,b for cubie-squares (facelets) to avoid confusion with cube Face notation.
+% We  use the t, b notation for cubie-squares (facelets) to avoid confusion with cube Face notation.
 % We number the cubie-squares on a face 1--9 reading from left-to-right, 
 % starting top-left, ending bottom-right, as follows 
 % (see also Figure~\ref{fig:facenotation}): 
 % {\newline}\strut\hspace{1cm}top row \ \ \ \ \ (1,2,3) = tl, tm, tr
-% {\newline}\strut\hspace{1cm}middle row (4,5,6) = ml, mm, mr
+% {\newline}\strut\hspace{1cm}middle row\, (4,5,6) = ml, mm, mr
 % {\newline}\strut\hspace{1cm}bottom row (7,8,9) = bl, bm, br
 %
 %  \begin{macro}{\RubikFaceUp} 
@@ -2936,12 +4018,12 @@
 % Each letter is an initial letter of the words Up, Down, Left, Right, Front, Back, 
 % left, middle, right, top, middle, bottom. 
 %
-% For example, in the command \cmd{\Urt\{\#1\}} 
+% For~example, in the command \cmd{\Urt\{\#1\}} 
 % the U stands for the Up face of the cube, while the \texttt{rt} stands 
 % for the ``right-top'' facelet on this face. Note that the order 
-% of the two lowercase letters (in this case \texttt{rt}) are always written 
-% in the $x,y$ order; i.e.,~the first of the two lowercase letters relates to the $x$ 
-% direction (either left, middle, or right), while the second  lowercase letter 
+% of the two lower-case letters (in this case \texttt{rt}) are always written 
+% in the $x,y$ order; i.e.,~the first of the two lower-case letters relates to the $x$ 
+% direction (either left, middle, or right), while the second  lower-case letter 
 % relates to the $y$  direction (either top, middle, or bottom)---this rule makes it
 % easy to remember the order.
 %  \end{macro}
@@ -2989,9 +4071,11 @@
 %  \begin{macro}{\RubikFaceRightAll} 
 %  \begin{macro}{\RubikFaceFrontAll}  
 %  \begin{macro}{\RubikFaceBackAll}  
-% These 5 commands allocate the same colour to all 9 cubiesquares in the specified face (Up, Down, Left, Right, Front).  Each command therefore  takes only  1 argument (one of the colour codes).
+% These 5 commands allocate the same colour to all 9 cubie-squares 
+% in the specified face (Up, Down, Left, Right, Front).  
+% Each command therefore  takes only  1~argument (one of the colour codes).
 %
-% {\noindent}For example, \cmd{\RubikFaceUpAll\{R\}}
+% {\noindent}For~example, \cmd{\RubikFaceUpAll\{R\}}
 %  \end{macro}
 %  \end{macro}
 %  \end{macro}
@@ -3031,7 +4115,8 @@
 }
 %    \end{macrocode}
 %
-% {\noindent}We now use these commands to initialise all visible faces to  default colour grey (X)
+% {\noindent}Finally, we now use these commands to initialise all 
+% visible faces to the default colour grey~(X)
 %
 % \begin{macrocode}
 \RubikFaceUpAll{X}%
@@ -3051,7 +4136,9 @@
 %    \begin{macro}{\RubikCubeGrey}
 % This command sets the face/colour configuration (state) of a 3x3x3 
 % Rubik cube with no colours allocated except for the central cubie of each face.
-% These central colours match those defined for the RubikCubeSolved command. 
+% The colour configuration of the central cubies matches those defined for 
+% the RubikCubeSolved command (i.e.,~white opposite yellow etc). 
+% We also implement an equivalent `gray' version (to be consistent with TikZ).
 %    \begin{macrocode}
 \newcommand{\RubikCubeGrey}{%
 \RubikFaceUp   {X}{X}{X}{X}{W}{X}{X}{X}{X}%
@@ -3061,29 +4148,73 @@
 \RubikFaceFront{X}{X}{X}{X}{O}{X}{X}{X}{X}%
 \RubikFaceBack {X}{X}{X}{X}{R}{X}{X}{X}{X}%
 }
+\newcommand{\RubikCubeGray}{\RubikCubeGrey}
 %    \end{macrocode}
 %    \end{macro}
 %
 %
-%   \subsection{\hspace{3mm}RubikCubeSolved command}
 %
-%    \begin{macro}{\RubikCubeSolved}
+%
+%   \subsection{\hspace{3mm}SolvedConfig command}
+%
+%    \begin{macro}{\SolvedConfig}
 % This command sets the face/colour configuration (state) of a  typical 
-% solved Rubik cube. 
+% solved Rubik cube. Note that the order is Right, Left, Up, Down, Front, Back 
+% (i.e.,~X$+$, X$-$, Y$+$, Y$-$, Z$+$, Z$-$, order). 
+%  We shall use this command to define solved cube configurations.
 %    \begin{macrocode}
-\newcommand{\RubikCubeSolved}{%
-  \RubikFaceUpAll{W}%
-  \RubikFaceDownAll{Y}%
-  \RubikFaceLeftAll{B}%
-  \RubikFaceRightAll{G}%
-  \RubikFaceFrontAll{O}%
-  \RubikFaceBackAll{R}%
+\newcommand{\SolvedConfig}[6]{%
+  \RubikFaceRightAll{#1}%
+  \RubikFaceLeftAll{#2}%
+  \RubikFaceUpAll{#3}%
+  \RubikFaceDownAll{#4}%
+  \RubikFaceFrontAll{#5}%
+  \RubikFaceBackAll{#6}%
 }
 %    \end{macrocode}
 %    \end{macro}
 %
 %
 %
+%
+%   \subsection{\hspace{3mm}RubikCubeGreyAll command}
+%    \label{sec:codegreyall}
+%
+%    \begin{macro}{\RubikCubeGreyAll}
+% This command sets the face/colour configuration (state) of a 3x3x3 
+% Rubik cube  with no colours allocated.
+% This colour configuration is the same as the startup default state---all cubies will
+% appear grey. We implement it using the \cmd{\SolvedConfig} command (above).
+% We also implement an equivalent `gray' version (to be consistent with TikZ).
+%    \begin{macrocode}
+\newcommand{\RubikCubeGreyAll}{\SolvedConfig{X}{X}{X}{X}{X}{X}}%
+\newcommand{\RubikCubeGrayAll}{\RubikCubeGreyAll}
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+%   \subsection{\hspace{3mm}RubikCubeSolved command}
+%     \label{sec:codesolvedconfig}
+%
+%    \begin{macro}{\RubikCubeSolved}
+%    \begin{macro}{\RubikCubeSolvedWY}
+%    \begin{macro}{\RubikCubeSolvedWB}
+% The first (default) command sets the face/colour configuration (state) one of the standard 
+% commercially available solved Rubik cube (white opposite yellow). The argument order
+% follows the XYZ notation. For convenience we make a copy named \cmd{\RubikCubeSolvedWY} 
+% (denoting  the White opposite Yellow configuration), and also a different version named 
+% \cmd{\RubikCubeSolvedWB} (denoting the White opposite Blue configuration).
+% These represent the two standard versions of the Rubik Cube.
+%    \begin{macrocode}
+\newcommand{\RubikCubeSolved}{\SolvedConfig{G}{B}{W}{Y}{O}{R}}%
+\newcommand{\RubikCubeSolvedWY}{\RubikCubeSolved}%
+\newcommand{\RubikCubeSolvedWB}{\SolvedConfig{R}{O}{W}{B}{G}{Y}}%
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
 %         \subsection{\hspace{3mm}Slice commands}
 %
 % \begin{macro}{\RubikSliceTopR} 
@@ -3148,7 +4279,7 @@
 % and \TeX\ has only 9 macro  parameters available, we are forced to draw 
 % Rubik cubes  by first specifying the colours on each of the three faces, 
 % and then  using a `DrawRubikCubeXY' command, where the trailing XY code
-%  defines the  view direction (X = either R, L; Y = either U, D). 
+%  defines the  viewing  direction (X = either R or L; Y = either U or D). 
 % The order of the XY code is important: X~first, Y~second (so it is easy to remember).
 %
 % On each face the facelets are drawn in the following order: Top row 
@@ -3158,7 +4289,7 @@
 % through the  four corners of the facelet in the following order: 
 % lb $\rightarrow$ lt $\rightarrow$ rt $\rightarrow$ rb;  the code being 
 % lb (LeftBottom), lt (LeftTop), rt (RightTop), rb (RightBottom)
-% (only need four coords); the grid origin is at the bottom-left corner of the 
+% (only need four coords); the (x,y) grid origin is at the bottom-left corner of the 
 % \textsc{front} face.
 %
 %  \begin{macro}{\DrawRubikCubeFrontFace}
@@ -3197,7 +4328,7 @@
 %      \subsubsection{\hspace{3mm}Viewing direction}
 %
 %  The command  `DrawRubikCubeXY' command uses the trailing XY code
-%  to specify  the  view direction (X = either R, L; Y = either U, D). 
+%  to specify  the  view direction (X = either R or L; Y = either U or D). 
 %  The order of the XY code is important: X~first, Y~second (so it is easy
 %  to remember).
 %
@@ -3209,7 +4340,8 @@
 % The colours are allocated  to particular facelets using  the   \cmd{\RubikFaceUp},
 %  \cmd{\RubikFaceRight} and  \cmd{\RubikFaceFront} commands. 
 %
-% The (x,y) grid origin is at the bottom-left corner of the \textsc{front} face.
+% The (x,y) grid origin is at the bottom-left corner of the \textsc{front} face 
+% (see Section~\ref{sec:coordinates}).
 % The perspective is designed so that the  2D~graphic image of the  side face 
 % (\textsc{right} in this particular case) has its `horizontal' lines running 
 % at 45~degrees. This has the useful advantage that the 2D~width of the side is 
@@ -3450,9 +4582,10 @@
 %   These two LayerFace commands each draw and paint a single  
 %  face of 9~facelets. The first command takes 9 ordered colour parameters,
 %  (ordered in layers from top left to bottom right, so \texttt{\#1} 
-%  is the placeholder for the colour of the TopLeft facelet etc.)
-%  The second takes only one colour parameter (since \texttt{All} the 
+%  is the place-holder for the colour of the TopLeft facelet etc.)
+%  The second command takes only one colour parameter (since \texttt{All} the 
 %  colours are the same).
+%
 %  The drawing origin (0,0) = bottom left corner. The facelets are drawn
 %  from left to right.
 %  NOTE: this macro is SAME as the  internal command 
@@ -3517,8 +4650,12 @@
 %
 % [\textsc{note}: These new commands (version 3.0) were modified from the 
 %  earlier \cmd{\FlatUp}, \cmd{\FlatDown} etc., commands; i.e.,~they were 
-%  reformulated as  a set of \cmd{\Draw...} commands to make them consistent 
-%  with all the  other \cmd{\Draw..} commands].
+%  reformulated as  a set of \cmd{\Draw...} commands so as to make this 
+%  notation consistent  with the  other \cmd{\Draw..} commands. 
+%  Note also that, for user convenience, all of these commands have 
+%  been copied (in version~4.0) to equivalent \cmd{\DrawFace..} 
+%  versions associated with their two coordinate arguments 
+%  set to  $x=0$, $y=0$---see Section~\ref{sec:drawfacecode}]
 %
 %  \begin{macro}{\DrawFlatUp}
 %  \begin{macro}{\DrawFlatDown}
@@ -3526,11 +4663,13 @@
 %  \begin{macro}{\DrawFlatRight}
 %  \begin{macro}{\DrawFlatFront}
 %  \begin{macro}{\DrawFlatBack}
-%  Each of these  commands draws a separate (flat) face (9~facelets).
+%  Each of these  commands draws a separate (flat) face (9~facelets)
+%  (see Section~\ref{sec:flatcommands}).
 %  Each command (except \cmd{\DrawFlatFront}) takes two arguments, 
 %  namely the  X-coordinate  and Y-coordinate of the bottom-left 
 %  corner of the  face.  This (X,Y) pair of coordinates therefore allows 
-%  the user to position the face. These commands were motivated by a need to 
+%  the user to position the face in relation to the cube itself. 
+%  These commands were motivated by a need to 
 %  be able to show hidden faces under certain circumstances.
 %
 %  Note  that the Y-argument currently only works fully
@@ -3553,9 +4692,9 @@
 %  of a Rubik cube.
 %
 % The (x,y) variables are here encoded as (\cmd{\ux}, \cmd{\uy})  where the 
-% `u' stands for Up etc. However, since we are unable to use `dx, dy' with the 
-%  \cmd{\DrawFlatDown} command (since dx and dy are already used in the 
-% \cmd{\cube@dxdydz...} command) we encode these instead as (\cmd{\ddx}, \cmd{\ddy}). 
+% `u' stands for Up etc. However, since we are unable to use a `dx, dy' notation
+%  with the   \cmd{\DrawFlatDown} command (since dx and dy are already used by the 
+% \cmd{\cube@dxdydz...} command), we encode these instead as (\cmd{\ddx}, \cmd{\ddy}). 
 %
 % \end{macro}
 % \end{macro}
@@ -3689,7 +4828,7 @@
 }
 %%-----------------------
 \newcommand{\DrawFlatFront}{%
-%% This command is used /only/ by  the \cmd{\DrawRubikFlat} command.
+%% This command is used /only/ by  the \cmd{\DrawRubikCubeF} command.
 %% NOTE: x, y variables not implemented as not required here
 %%---top row
 \draw[line join=round,line cap=round,ultra thick,fill=\Flt]%
@@ -3756,12 +4895,12 @@
 }
 %    \end{macrocode}
 %
-%  \begin{macro}{\DrawRubikFlat}
-%  Draws a standard flat representation of the Rubik
-%  cube (colours only). Note that \cmd{\DrawFlatFront} does not 
-%  take any arguments (x,y) arguments.
+%  \begin{macro}{\DrawRubikCubeF}
+%  Draws a standard flat (F) representation of the Rubik
+%  cube (colours only). Note that \cmd{\DrawFlatFront} (below)
+%  does not take any arguments (x,y). 
 %    \begin{macrocode}
-\newcommand{\DrawRubikFlat}{%
+\newcommand{\DrawRubikCubeF}{%
   \DrawFlatUp{0}{3}%
   \DrawFlatDown{0}{-3}%
   \DrawFlatLeft{-3}{0}%
@@ -3772,12 +4911,13 @@
 %    \end{macrocode}
 %  \end{macro}
 %
-%  \begin{macro}{\DrawRubikCubeFlat}
+%
+%  \begin{macro}{\DrawRubikCubeSF}
 %  Draws a Rubik  cube together with the three hidden faces
-%   (colours only) in a semi-flat representation. The (x,y) 
-%  arguments are for the bottom-left  corner of the face.
+%   (colours only) in a semi-flat (SF) representation. The (x,y) 
+%  arguments (below) are for the bottom-left  corner of the face. 
 %    \begin{macrocode}
-\newcommand{\DrawRubikCubeFlat}{%
+\newcommand{\DrawRubikCubeSF}{%
   \DrawRubikCube%
   \DrawFlatDown{0}{-3}%
   \DrawFlatLeft{-3}{0}%
@@ -3789,6 +4929,7 @@
 %
 %
 % \subsubsection{DrawFlatXSide commands}
+%  \label{sec:drawflatxsidecode}
 %
 %  These six commands draw  a face together with  all four sidebars
 %  (colours only). We use the \cmd{\DrawFlatX} commands to draw the face.
@@ -3798,7 +4939,10 @@
 %  Top (T) and Bottom (B) = left to right;
 %  Left (L) and Right (R) = top to bottom;
 % (see the \cmd{\DrawRubikLayerSideX} command for details of the arguments).
-%  
+% 
+% Note that for user convenience, we we have copied many of these commands 
+% to a \cmd{\DrawFace..} version (see Section~\ref{sec:drawfacecode}).
+% 
 %
 %  \begin{macro}{\DrawFlatUpSide}
 %  Draws the \textsc{up} face together with  all four sidebars
@@ -3891,6 +5035,31 @@
 %
 %
 %
+%   \subsection{\hspace{3mm}DrawFace commands}
+%  \label{sec:drawfacecode}
+%
+% We now copy the above \cmd{\DrawFlat..} commands
+% as \cmd{\DrawFace..} commands  for the purpose of user
+% convenience, since most of the time the user  wants just to
+% draw a particular face with or without the associated side bars.
+% In a future version we may well, therefore, deprecate some of the above 
+% `Flat'  command names.
+%    \begin{macrocode}
+\newcommand{\DrawFaceUp}{\DrawFlatUp{0}{0}}
+\newcommand{\DrawFaceDown}{\DrawFlatDown{0}{0}}
+\newcommand{\DrawFaceLeft}{\DrawFlatLeft{0}{0}}
+\newcommand{\DrawFaceRight}{\DrawFlatRight{0}{0}}
+\newcommand{\DrawFaceFront}{\DrawFlatFront{0}{0}}
+\newcommand{\DrawFaceBack}{\DrawFlatBack{0}{0}}
+\newcommand{\DrawFaceUpSide}{\DrawFlatUpSide}
+\newcommand{\DrawFaceDownSide}{\DrawFlatDownSide}
+\newcommand{\DrawFaceLeftSide}{\DrawFlatLeftSide}
+\newcommand{\DrawFaceRightSide}{\DrawFlatRightSide}
+\newcommand{\DrawFaceFrontSide}{\DrawFlatFrontSide}
+\newcommand{\DrawFaceBackSide}{\DrawFlatBackSide}
+%    \end{macrocode}
+%
+%
 %   \subsection{\hspace{3mm}SideBar commands}
 %
 %  SideBar commands draw narrow bars of colour indicating  the 
@@ -3949,7 +5118,7 @@
 % Note that the TikZ \cmd{\pgfmathsetmacro} commands (which do the maths)
 %  must be inside  the TeX sidebar command in order to work.
 % The start point of the TikZ \cmd{\draw} command for  each bar rectangle 
-%    is botton Left corner of the bar =(\cmd{\dx},\cmd{\dy})
+%    is bottom Left corner of the bar =(\cmd{\dx},\cmd{\dy})
 % \end{macro}
 % \end{macro}
 % \end{macro}
@@ -3999,15 +5168,15 @@
 % Right, Top, Middle, Bottom, x, y, as follows:
 % \begin{quote}
 %  X$_1$  is an $x$ parameter: either $\langle L\mid M \mid  R\rangle$
-%  {\newline}X$_2$  is an $y$ parameter: either $\langle T\mid M \mid  B\rangle$
+%  {\newline}X$_2$  is a \, $y$ parameter: either $\langle T\mid M \mid  B\rangle$
 %  {\newline}X$_3$  is an extra parameter: either $\langle x\mid y \rangle$,
 %  required by corner sidebars to indicate whether the sidebar was either 
 %  above or below $\langle y \rangle$, or to the left or 
 %  right $\langle x \rangle$ of the associated  cubie.
 % An $X_3$ parameter is not required for the sidebar of an edge cubie, since 
-% only one location is posible in these cases.
+% only one location is possible in these cases.
 % \end{quote}
-% For example, the following command
+% For~example, the following command
 % \begin{quote}
 %   \cmd{\DrawRubikLayerSideLTy\{G\}}
 % \end{quote}
@@ -4038,7 +5207,7 @@
 %    \end{macrocode}
 %
 %
-%  \subsubsection{\hspace{3mm}Drawing multiple cubie  sidebars}
+%  \subsubsection{\hspace{3mm}Drawing multiple cubie sidebars}
 %
 %    \begin{macro}{\DrawRubikLayerSideT}
 %    \begin{macro}{\DrawRubikLayerSideB}
@@ -4107,6 +5276,65 @@
 %  \end{macro}
 %
 %
+% \subsection{\hspace{3mm}RubikSide commands}
+% \label{sec:rubiksidecode}
+%
+%  \begin{macro}{\RubikSideLeft} 
+%  \begin{macro}{\RubikSideRight} 
+%  \begin{macro}{\RubikSideFront}  
+%  \begin{macro}{\RubikSideBack}  
+%  RubikSide commands allocate colours to the side facelets of the 
+%  UP~face---see Section~\ref{sec:rubikside}.
+%  These facelets are the top three facelets of each side Front, Back, Left, Right.
+%    \begin{macrocode}
+\newcommand{\RubikSideFront}[3]{%
+\def\Flt{#1}\def\Fmt{#2}\def\Frt{#3}% 
+}
+\newcommand{\RubikSideRight}[3]{%
+\def\Rlt{#1}\def\Rmt{#2}\def\Rrt{#3}% 
+}
+\newcommand{\RubikSideLeft}[3]{%
+\def\Llt{#1}\def\Lmt{#2}\def\Lrt{#3}% 
+}
+\newcommand{\RubikSideBack}[3]{%
+\def\Blt{#1}\def\Bmt{#2}\def\Brt{#3}% 
+}
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro} 
+%  \end{macro}
+%  \end{macro}
+%
+%
+%  \begin{macro}{\RubikSideLeftAll} 
+%  \begin{macro}{\RubikSideRightAll} 
+%  \begin{macro}{\RubikSideFrontAll}  
+%  \begin{macro}{\RubikSideBackAll}  
+% These 4 commands allocate the same colour to all 3 cubiesquares in the specified face 
+% (Left, Right, Front, Back).  Each command therefore  takes only  1 argument 
+% (one of the colour codes).
+%
+% {\noindent}For~example, \cmd{\RubikSideUpAll\{R\}}
+%    \begin{macrocode}
+\newcommand{\RubikSideFrontAll}[1]{%
+\def\Flt{#1}\def\Fmt{#1}\def\Frt{#1}% 
+}
+\newcommand{\RubikSideRightAll}[1]{%
+\def\Rlt{#1}\def\Rmt{#1}\def\Rrt{#1}% 
+}
+\newcommand{\RubikSideLeftAll}[1]{%
+\def\Llt{#1}\def\Lmt{#1}\def\Lrt{#1}% 
+}
+\newcommand{\RubikSideBackAll}[1]{%
+\def\Blt{#1}\def\Bmt{#1}\def\Brt{#1}% 
+}
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro} 
+%  \end{macro}
+%  \end{macro}
+%
+%
 %
 %    \subsection{\hspace{3mm}NCube command}
 %
@@ -4123,7 +5351,7 @@
 % The command takes four ordered  arguments, as follows:
 % \begin{quote}
 %   \#1 = number of cubies ($n>0$) along each side,
-%   {\newline}\#2, \#3, \#4 = colors of the visible faces (in X,Y,Z order);
+%   {\newline}\#2, \#3, \#4 = colours of the visible faces (in X,Y,Z order);
 %             X=Right face  colour, Y=Up face colour, Z=Front face colour.
 % \end{quote}
 % We use the  \cmd{\pgfmathsetmacro}\marg{variable-name}\marg{numeric value or maths}
@@ -4144,10 +5372,11 @@
 %    \end{macro}
 %
 %   \begin{macro}{\cube@dxdydz}
-% This internal command is  used only by the \cmd{\DrawNCubeAll} command.
-% The original version of this command was developed  by Peter Bartal (see Bartal, 2011).
-% It was modified (2012) by RWD Nickalls (to implement  a more 
-% intuitive X, Y, Z ordering of parameters).
+% This internal command is  used only by the \cmd{\DrawNCubeAll} command 
+% (see above).  The original version of this command was developed  
+% by Peter Bartal (see Bartal, 2011).
+% It was later modified (2012) by RWD Nickalls (to implement  a more 
+% intuitive X, Y, Z ordering of the face colour parameters).
 %
 %  The cube need not be in the origin, the distances of 
 % the \textsc{down}-behind [L] corner from 
@@ -4175,7 +5404,7 @@
 % options to  each of the TikZ  \cmd{\draw} commands, in order to improve 
 % the line joining (first two options); (2) adjusted  the \cmd{\cube@dxdydz} macro 
 % to adopt the ordered  XYZ face colour notation
-% (by reassigning \#2, \#3, \#4).
+% (by reassigning \#2, \#3, \#4  to the X, Y, Z face colours, as shown above).
 %
 %    \begin{macrocode}
 \newcommand{\cube@dxdydz}[7]{%
@@ -4192,7 +5421,7 @@
     \draw[line join=round,line cap=round,ultra thick,fill=#4]%
  (#5,#6,\dz) -- (\dx,#6,\dz) -- (\dx,\dy,\dz) -- (#5,\dy,\dz) -- cycle;
 %% The 'rectangle' command does not work with 3D coordinates, 
-%% so this is the way to draw the squres with space coordinates
+%% so this is the way to draw the squares with space coordinates
 %% Draw UP face (using the Y colour = #3)
    \draw[line join=round,line cap=round,ultra thick,fill=#3]%
  (#5,\dy,\dz) -- (\dx,\dy,\dz) -- (\dx,\dy,#7) -- (#5,\dy,#7) -- cycle;
@@ -4214,10 +5443,10 @@
 %  (adjust \texttt{cy}) and horizontal viewpoint  (adjust \texttt{cx})
 %  of a single cubie (described in more detail in the \rubikcube\ 
 %   package  documentation).
-%  Note that we cannot use the names \texttt{dx}, \texttt{dy} for variables since 
-%  these have been  allocated already (see above). However, we do use 
-%  \texttt{dx}, \texttt{dy} in the  command names  as these will be more 
-%  readily understood by the user.
+%  Note that we cannot use the names \texttt{dx}, \texttt{dy} for the 
+%  variables here since  these names have been  allocated already 
+%  (see above). However, we can  use  \texttt{dx}, \texttt{dy} in the  
+%  command names  as these will be more  readily understood by the user.
 %    \begin{macrocode}
 \newcommand{\Cubiedx}[1]{\pgfmathsetmacro{\cx}{#1}}
 \newcommand{\Cubiedy}[1]{\pgfmathsetmacro{\cy}{#1}}
@@ -4307,8 +5536,8 @@
 %
 %  As before, the viewpoint is specified using an appended 
 % two-letter XY ordered viewpoint code: either RU, RD, LU, LD.
-% These commands take three arguments, namely three different XYZ 
-% ordered colour codes (R,O,Y,G,B,W,X).
+% These commands take three arguments (since just three faces are visible with this 
+% cube format), namely three different XYZ  ordered colour codes (R,O,Y,G,B,W,X).
 % \newline\textsc{format}: \cmd{\textCubieRU}\marg{Xcolour}\marg{Ycolour}\marg{Zcolour}
 % \newline\textsc{usage}: |\textCubieRU{G}{B}{W}|
 %    \end{macro}
@@ -4361,27 +5590,50 @@
 %
 %  \subsubsection{\hspace{3mm}Introduction}
 %
-%  We use a special prefix notation to denote each of four different repreresentations 
-% of the  various  Rubik cube rotations as follows: the name of the rotation (rr), its 
+%  We use a special prefix notation to denote each of four different representations 
+% of the  various  Rubik cube rotations as follows: the name of the Rubik rotation (rr), its 
 % associated hieroglyph (rrh), and combinations of name and hieroglyph both vertical (Rubik)
 % and horizontal (textRubik). A rotation command is a combination of a rotation-code appended 
 % to one of the four prefixes.
 %
-%  For example, the command \cmd{\rrhD}  generates the hieroglyph (rrh) associated with 
+%  For~example, the command \cmd{\rrhD}  generates the hieroglyph (rrh) associated with 
 % the rotation-code D. In this form it is used internally, but it is also available for the user.
-% However, it is also made available to the user in the more  intuitive form
-% |\rrh{D}| by the use of the internal macro |\@join| (see Sections~\ref{sec:cmdsusingjoin} 
-% and \ref{sec:usefulinternalcommands}).
+%
+% In version~3.0, however, all the rotation commands were also made available to the user 
+% in the much more  intuitive form  stem\{argument\} form, for~example,  
+% |\rrh{D}|. In practice, this `argument' form actually generates the original non-argument 
+% form by the use of the internal macro |\@join|. 
+% For example, \verb!\rrh{D}! $\rightarrow$ join(\verb!\rrh! + \verb!D!) $\rightarrow$ \verb!\rrhD! 
+% (see Sections~\ref{sec:cmdsusingjoin} for details).
 % 
-% The square hieroglyphs are built up in stages. We first create an internal 
-% command  for drawing the square (\cmd{\DrawNotationBox}), and then draw the 
-% contents (lines, arrows, arcs of circles, and sometimes just text).
-% (for the TikZ  ARC command see  TikZ pgfmanual (2012)  page~146 (\S 14.8)).
+% The hieroglyphs are of two types: `arrow' glyphs (all exactly square),
+%  and `letter' glyphs  (mostly square, but many are rectangular); however both 
+% types are  made to have the same  height so they sit nicely when arranged side-by-side. 
+% A lot of special macros for handling and generating these glyphs are described below
+%  in Section~\ref{sec:usefulinternalcommands} (and also in Section~\ref{sec:codedrawnotationbox}).
+%
+% The `arrow'  hieroglyphs are built up in stages using TikZ. We first create a 
+% command  for drawing the square (\cmd{\DrawNotationBox}; 
+% see Section~\ref{sec:codedrawnotationbox}) and then draw the 
+% contents (lines, arrows, arcs of circles). For an example, 
+% see the D~form \rrh{D}\ constructed in  Section~\ref{sec:coderotationD}.
+%
+% The `letter' hieroglyphs (glyphs for which the rotations cannot be seen from the front, 
+% and  hence cannot have arrows) just give a letter representation of the rotation 
+% (say, Bw for `back wide'). These glyphs are therefore made using  an fbox (for convenience),
+%  and therefore these are sometimes not square. Some vertical fine-tuning using  
+% the \verb!\raisebox!  command is often required to force these  `letter' glyphs to
+% have the same vertical position as their  `arrow' cousins. For an example, 
+% see the form \rrh{Bw}\ constructed Section~\ref{sec:coderotationBw}).
 %
 %  The presence of small overfilled \cmd{\hbox}es associated with these squares
 % were originally checked using the \texttt{ltugboat.cls}, and all fixed mainly
 % by setting the associated  minipages $\rightarrow$ width = 0.6cm, 
 %  and using TikZ scale=0.5.
+%
+%
+%   \subsubsection{\hspace{3mm}DrawNotationBox}
+%  \label{sec:codedrawnotationbox}
 % 
 %
 %   \begin{macro}{\DrawNotationBox}
@@ -4389,7 +5641,7 @@
 % Note that we start at (0,0) and draw to the final point 
 % in order to make a nice corner join.
 %
-% TODO: ? make this a proper internal command 
+% todo: ? make this a proper internal command 
 % using \verb!@! sometime.
 %
 %   \begin{macrocode}
@@ -4403,10 +5655,11 @@
 % (e.g.,~\cmd{\@sd}, \cmd{\@sh} \ldots\ etc.) which will be required
 % for use in drawing the various lines and arrows.
 % Some hieroglyphs contain either one circular arc, or two concentric arcs, 
-% and these arcs require both a center and a start point. 
+% and these arcs require both a centre and a start point. 
 % Note that the final argument does not use any units.
+% For the TikZ  ARC command see  TikZ pgfmanual (2012)  page~146 (\S 14.8).
 %
-% TODO: make a small  diagram to illustrate the position of these 
+% todo: make a small  diagram to illustrate the position of these 
 % parameters and make things a  bit clearer sometime.
 % 
 %\begin{macrocode}
@@ -4422,23 +5675,148 @@
 \pgfmathsetmacro{\@sqcy}{\@scy+0.25} %% SQuare CenterY cpprd
 %    \end{macrocode}
 %
-%  All the \verb!@! internal commands used in the following  commands 
-% and macros are described in Section~\ref{sec:usefulinternalcommands}.
 %
 %
 %
-%  \subsubsection{\hspace{3mm}Using {\textbackslash}\texttt{join}}
+%   \subsubsection{\hspace{3mm}Some useful internal commands}
+%  \label{sec:usefulinternalcommands}
+%
+%  \begin{macro}{\@rr} 
+%  \begin{macro}{\@rrp}
+%  \begin{macro}{\@rrw} 
+%  \begin{macro}{\@rrwp} 
+%  \begin{macro}{\@rrs} 
+%  \begin{macro}{\@rrsp}
+%  \begin{macro}{\@rra} 
+%  \begin{macro}{\@rrap} 
+%  \begin{macro}{\@xyzh} 
+%  \begin{macro}{\@xyzhp} 
+%  \begin{macro}{\@xyzRubik} 
+%  \begin{macro}{\@xyzRubikp} 
+%  \begin{macro}{\@SquareLetter} 
+%  \begin{macro}{\@hRubik} 
+%  These internal commands are used to generate the
+% prime, w, w-prime, s, s-prime, a, a-prime   
+% rotation commands. The \cmd{\@xyz..} commands are used to generate the 
+% x, y, z, u, d, l, r, f, b commands and their associated prime rotation commands.
+% The \cmd{\@SquareLetter} command is used to form the separate square hieroglyph  form
+% used for rotations with no visible representation from the front 
+% (e.g.,~B.., Fs, Fsp, Fa, Fap, S, Sp, Sf, Sfp, Sb, Sbp).
+% The \cmd{\@hRubik} is the vertical shift  used  to raise the box carrying the rotation 
+% rotation-code in \cmd{\Rubik..} commands not visible from the front.
+%
+% The commands \verb!\@xyzhbdfl! and  \verb!\@xyzbdflRubik! relate to the 
+% axis rotations denoted as  b, d, f, l; since these four letters have long upstrokes
+% they require special fine-tuning for vertical position.
+%  
+%  The idea is that by using these internal
+% tools taking parameters we are able to more easily standardise the size 
+% and position of all the various glyphs. For details of the 
+% rubikfont and rubikprime see Section~\ref{sec:coderubikfont}).
+%
+% Note that the TikZ `thick' line code = 0.8pt (used in \cmd{\@SquareLetter}).
+%
+% \begin{macrocode}
+\newcommand{\@rr}[1]{{\@rubikfont #1}}
+\newcommand{\@rrp}[1]{{\@rubikfont #1\@rubikprime}}
+\newcommand{\@rrw}[1]{{\@rubikfont #1{\@rubikfontFNS w}}}
+\newcommand{\@rrwp}[1]{{\@rubikfont #1{\@rubikfontFNS w}\@rubikprime}}
+\newcommand{\@rrs}[1]{{\@rubikfont #1{\@rubikfontFNS s}}}
+\newcommand{\@rrsp}[1]{{\@rubikfont #1{\@rubikfontFNS s}\@rubikprime}}
+\newcommand{\@rra}[1]{{\@rubikfont #1{\@rubikfontFNS a}}}
+\newcommand{\@rrap}[1]{{\@rubikfont #1{\@rubikfontFNS a}\@rubikprime}}
+\newcommand{\@rru}[1]{{\@rubikfont #1{\@rubikfontFNS u}}}
+\newcommand{\@rrup}[1]{{\@rubikfont #1{\@rubikfontFNS u}\@rubikprime}}
+\newcommand{\@rrd}[1]{{\@rubikfont #1{\@rubikfontFNS d}}}
+\newcommand{\@rrdp}[1]{{\@rubikfont #1{\@rubikfontFNS d}\@rubikprime}}
+\newcommand{\@rrl}[1]{{\@rubikfont #1{\@rubikfontFNS l}}}
+\newcommand{\@rrlp}[1]{{\@rubikfont #1{\@rubikfontFNS l}\@rubikprime}}
+\newcommand{\@rrr}[1]{{\@rubikfont #1{\@rubikfontFNS r}}}
+\newcommand{\@rrrp}[1]{{\@rubikfont #1{\@rubikfontFNS r}\@rubikprime}}
+\newcommand{\@rrf}[1]{{\@rubikfont #1{\@rubikfontFNS f}}}
+\newcommand{\@rrfp}[1]{{\@rubikfont #1{\@rubikfontFNS f}\@rubikprime}}
+\newcommand{\@rrb}[1]{{\@rubikfont #1{\@rubikfontFNS b}}}
+\newcommand{\@rrbp}[1]{{\@rubikfont #1{\@rubikfontFNS b}\@rubikprime}}
+\newcommand{\@rrc}[1]{{\@rubikfont #1{\@rubikfontFNS c}}}
+\newcommand{\@rrcp}[1]{{\@rubikfont #1{\@rubikfontFNS c}\@rubikprime}}
+\newcommand{\@rrm}[1]{{\@rubikfont #1{\@rubikfontFNS m}}}
+\newcommand{\@rrmp}[1]{{\@rubikfont #1{\@rubikfontFNS m}\@rubikprime}}
+\newcommand{\@xyzh}[1]{[{\@rubikfont #1}]}    
+\newcommand{\@xyzhp}[1]{[{\@rubikfont #1\@rubikprime}]}
+\newcommand{\@xyzRubik}[1]{\raisebox{3.45pt}{[{\@rubikfont #1}]}}   
+\newcommand{\@xyzRubikp}[1]{\raisebox{3.45pt}{[{\@rubikfont #1\@rubikprime}]}} 
+\newcommand{\@xyzhbdfl}[1]{[\raisebox{-0.6pt}{{\@rubikfont #1}}]}
+\newcommand{\@xyzbdflRubik}[1]{\raisebox{3.45pt}{[\raisebox{-0.6pt}{{\@rubikfont #1}}]}}
+\newcommand{\@SquareLetter}[1]{\setlength{\fboxsep}{2.5pt}%
+  \setlength{\fboxrule}{0.8pt}%
+  \fbox{\rule[-1pt]{0pt}{8.5pt}\raisebox{-0.5pt}{#1}}}
+\newlength\@hRubik%
+\setlength{\@hRubik}{0.185cm}%
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%
+%
+%
+%   \begin{macro}{\@tlen}
+% Feb 2017 (RWDN): \ We also  need to define a small length for fine-tuning the default
+%  horizontal space between  a pair of `letter' hieroglyphs, eg~B (i.e.,~when no 
+% additional space has been added by the user), so that this matches that between a pair of 
+% `arrow' hieroglyphs. This length is inserted on both sides of the square frame. 
+%  This length is used in two settings: (a)~in `letter' hieroglyphs (for an example, 
+% see the definition of the macro \cmd{\SquareB} in Section~\ref{sec:coderotationB}), 
+% and in (b)~in `arrow' hieroglyphs (for an example, 
+% see the definition of the macro \cmd{\rrhD} in Section~\ref{sec:coderotationD}).
+%
+%\begin{macrocode}
+\newcommand{\@tlen}{\hspace{1pt}}%
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+%
+%  \begin{macro}{\@join} 
+%  We also require a macro for joining two strings  so we can convert
+%  a rotation-code, say U,  into a macro which typesets it in some form, say \cmd{\rrhU}.
+%  The following \cmd{\@join\{\}\{\}} command is by Christian Tellechea (many thanks\,!).
+%  {\newline}\textsc{usage}: \cmd{\@join\marg{command-stem}\marg{rotation-code}}. For~example, 
+%  to create the command \cmd{\rrhU} we would write |\@join{\rrh}{U}|, and hence 
+%  the command |\rrh{U}| is equivalent to \cmd{\rrhU} (see Section~\ref{sec:cmdsusingjoin}).
+%  {\newline}Since this macro is also useful for processing rotation-codes in a  list, 
+%  which may also include macros, it is important that |#2| is not detokenized.
+% \begin{macrocode}
+\newcommand*\@join[2]{%
+    \csname\expandafter\@gobble\string#1#2\endcsname}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%
+%
+%  \subsubsection{\hspace{3mm}Using {\textbackslash}\texttt{@join}}
 %  \label{sec:cmdsusingjoin}
 %
 %   \begin{macro}{\textRubik}
 %   \begin{macro}{\Rubik}
 %   \begin{macro}{\rr}
 %   \begin{macro}{\rrh}
-%  The following four commands typeset a single rotation, where the rotation-code (eg~U) is 
+%  The following four commands typeset a single rotation, where the rotation-code (e.g.,~U) is 
 % the argument (see Section~\ref{sec:overview}). As an example, the format for 
 %  the \cmd{\rrh\{\}} command is
 % \cmd{\rrh}\marg{rotation-code}. In practice, these four commands are really a 
-% sort of front-end for all the commands which follow this section. For example, the 
+% sort of front-end for all the commands which follow this section. For~example, the 
 % command \cmd{\rrh\{U\}} generates the command \cmd{\rrhU} which itself typesets the 
 % rotation hieroglyph for the rotation~U, etc. 
 %
@@ -4461,6 +5839,7 @@
 %
 %
 %  \subsubsection{\hspace{3mm}Rotation B}
+%    \label{sec:coderotationB}
 %
 %  \begin{macro}{\rrB}
 %  \begin{macro}{\SquareB}
@@ -4469,12 +5848,20 @@
 %  \begin{macro}{\textRubikB}
 %  These commands  all draw forms which denote the B (\textsc{back}-face) rotation.
 %  Not visible from the front.
+%
+%  Feb 2017 (RWDN): added the \cmd{\@tlen} length (= 1pt; defined above) to the 
+%  \cmd{\SquareB} command, and removed  the terminal \cmd{\,} space 
+%  from the rrhB, RubikB, textRubikB commands, and copied
+%  this action with all the subsequent Letter hieroglyphs (e.g.,~B, Bw,..).
+%  These minor changes were to improve the spacing between two Letter hieroglyphs, 
+%  and make it match that between two square  `arrow' hieroglyphs.
+%  The same changes were made to all the `letter' hieroglyphs.
 % \begin{macrocode}
 \newcommand{\rrB}{\@rr{B}}
-\newcommand{\SquareB}{\@SquareLetter{\rrB}}
-\newcommand{\rrhB}{\raisebox{-0.25mm}{\SquareB}\,}
-\newcommand{\RubikB}{\raisebox{\@hRubik}{\SquareB}\,}
-\newcommand{\textRubikB}{\rrhB\,}
+\newcommand{\SquareB}{\@tlen\@SquareLetter{\rrB}\@tlen}
+\newcommand{\rrhB}{\raisebox{-0.25mm}{\SquareB}}
+\newcommand{\RubikB}{\raisebox{\@hRubik}{\SquareB}}
+\newcommand{\textRubikB}{\rrhB}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -4494,10 +5881,10 @@
 %  Not visible from the front.
 % \begin{macrocode}
 \newcommand{\rrBp}{\@rrp{B}}
-\newcommand{\SquareBp}{\@SquareLetter{\rrBp}}
-\newcommand{\rrhBp}{\raisebox{-0.25mm}{\SquareBp}\,}
-\newcommand{\RubikBp}{\raisebox{\@hRubik}{\SquareBp}\,}
-\newcommand{\textRubikBp}{\rrhBp\,}
+\newcommand{\SquareBp}{\@tlen\@SquareLetter{\rrBp}\@tlen}
+\newcommand{\rrhBp}{\raisebox{-0.25mm}{\SquareBp}}
+\newcommand{\RubikBp}{\raisebox{\@hRubik}{\SquareBp}}
+\newcommand{\textRubikBp}{\rrhBp}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -4507,6 +5894,7 @@
 %
 %
 %  \subsubsection{\hspace{3mm}Rotation Bw}
+%  \label{sec:coderotationBw}
 %
 %  \begin{macro}{\rrBw}
 %  \begin{macro}{\SquareBw}
@@ -4516,12 +5904,11 @@
 %  These commands  all draw forms which denote the Bw rotation.
 %  Not visible from the front.
 % \begin{macrocode}
-%\newcommand{\rrBw}{\textbf{\textsf{Bw}}}
 \newcommand{\rrBw}{\@rrw{B}}
-\newcommand{\SquareBw}{\@SquareLetter{\rrBw}}
-\newcommand{\rrhBw}{\raisebox{-0.25mm}{\SquareBw}\,}
-\newcommand{\RubikBw}{\raisebox{\@hRubik}{\SquareBw}\,}
-\newcommand{\textRubikBw}{\rrhBw\,}
+\newcommand{\SquareBw}{\@tlen\@SquareLetter{\rrBw}\@tlen}
+\newcommand{\rrhBw}{\raisebox{-0.25mm}{\SquareBw}}
+\newcommand{\RubikBw}{\raisebox{\@hRubik}{\SquareBw}}
+\newcommand{\textRubikBw}{\rrhBw}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -4540,12 +5927,11 @@
 %  These commands  all draw forms which denote the Bwp rotation.
 % Not visible from the front.
 % \begin{macrocode}
-%\newcommand{\rrBwp}{\textbf{\textsf{Bwp}}}
 \newcommand{\rrBwp}{\@rrwp{B}}
-\newcommand{\SquareBwp}{\@SquareLetter{\rrBwp}}
-\newcommand{\rrhBwp}{\raisebox{-0.25mm}{\SquareBwp}\,}
-\newcommand{\RubikBwp}{\raisebox{\@hRubik}{\SquareBwp}\,}
-\newcommand{\textRubikBwp}{\rrhBwp\,}
+\newcommand{\SquareBwp}{\@tlen\@SquareLetter{\rrBwp}\@tlen}
+\newcommand{\rrhBwp}{\raisebox{-0.25mm}{\SquareBwp}}
+\newcommand{\RubikBwp}{\raisebox{\@hRubik}{\SquareBwp}}
+\newcommand{\textRubikBwp}{\rrhBwp}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -4564,12 +5950,11 @@
 %  These commands  all draw forms which denote the Bs rotation.
 %  Not visible from the front.
 % \begin{macrocode}
-%\newcommand{\rrBs}{\textbf{\textsf{Bs}}}
 \newcommand{\rrBs}{\@rrs{B}}
-\newcommand{\SquareBs}{\@SquareLetter{\rrBs}}
-\newcommand{\rrhBs}{\raisebox{-0.25mm}{\SquareBs}\,}
-\newcommand{\RubikBs}{\raisebox{\@hRubik}{\SquareBs}\,}
-\newcommand{\textRubikBs}{\rrhBs\,}
+\newcommand{\SquareBs}{\@tlen\@SquareLetter{\rrBs}\@tlen}
+\newcommand{\rrhBs}{\raisebox{-0.25mm}{\SquareBs}}
+\newcommand{\RubikBs}{\raisebox{\@hRubik}{\SquareBs}}
+\newcommand{\textRubikBs}{\rrhBs}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -4588,12 +5973,11 @@
 %  These commands  all draw forms which denote the Bsp rotation.
 %  Not visible from the front.
 % \begin{macrocode}
-%\newcommand{\rrBsp}{\textbf{\textsf{Bsp}}}
 \newcommand{\rrBsp}{\@rrsp{B}}
-\newcommand{\SquareBsp}{\@SquareLetter{\rrBsp}}
-\newcommand{\rrhBsp}{\raisebox{-0.25mm}{\SquareBsp}\,}
-\newcommand{\RubikBsp}{\raisebox{\@hRubik}{\SquareBsp}\,}
-\newcommand{\textRubikBsp}{\rrhBsp\,}
+\newcommand{\SquareBsp}{\@tlen\@SquareLetter{\rrBsp}\@tlen}
+\newcommand{\rrhBsp}{\raisebox{-0.25mm}{\SquareBsp}}
+\newcommand{\RubikBsp}{\raisebox{\@hRubik}{\SquareBsp}}
+\newcommand{\textRubikBsp}{\rrhBsp}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -4612,12 +5996,11 @@
 %  These commands  all draw forms which denote the Ba rotation.
 % Not visible from the front.
 % \begin{macrocode}
-%\newcommand{\rrBa}{\textbf{\textsf{Ba}}}
 \newcommand{\rrBa}{\@rra{B}}
-\newcommand{\SquareBa}{\@SquareLetter{\rrBa}}
-\newcommand{\rrhBa}{\raisebox{-0.25mm}{\SquareBa}\,}
-\newcommand{\RubikBa}{\raisebox{\@hRubik}{\SquareBa}\,}
-\newcommand{\textRubikBa}{\rrhBa\,}
+\newcommand{\SquareBa}{\@tlen\@SquareLetter{\rrBa}\@tlen}
+\newcommand{\rrhBa}{\raisebox{-0.25mm}{\SquareBa}}
+\newcommand{\RubikBa}{\raisebox{\@hRubik}{\SquareBa}}
+\newcommand{\textRubikBa}{\rrhBa}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -4636,12 +6019,11 @@
 %  These commands  all draw forms which denote the Bap rotation.
 % Not visible from the front.
 % \begin{macrocode}
-%\newcommand{\rrBap}{\textbf{\textsf{Bap}}}
 \newcommand{\rrBap}{\@rrap{B}}
-\newcommand{\SquareBap}{\@SquareLetter{\rrBap}}
-\newcommand{\rrhBap}{\raisebox{-0.25mm}{\SquareBap}\,}
-\newcommand{\RubikBap}{\raisebox{\@hRubik}{\SquareBap}\,}
-\newcommand{\textRubikBap}{\rrhBap\,}
+\newcommand{\SquareBap}{\@tlen\@SquareLetter{\rrBap}\@tlen}
+\newcommand{\rrhBap}{\raisebox{-0.25mm}{\SquareBap}}
+\newcommand{\RubikBap}{\raisebox{\@hRubik}{\SquareBap}}
+\newcommand{\textRubikBap}{\rrhBap}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -4651,6 +6033,7 @@
 %
 %
 %  \subsubsection{\hspace{3mm}Rotation D}
+%   \label{sec:coderotationD}
 %
 %  \begin{macro}{\rrD}
 %  \begin{macro}{\SquareD}
@@ -4658,8 +6041,12 @@
 %  \begin{macro}{\RubikD}
 %  \begin{macro}{\textRubikD}
 %  These commands  all draw forms which denote the D rotation.
+%
+%  Feb 2017 (RWDN): \ added the  \cmd{\@tlen} length to the \cmd{\rrhD} command to improve the 
+%  spacing between two `arrow' square hieroglyphs; and also removed the terminal \cmd{\,}
+%  space. The same changes were made to all the `arrow' hieroglyphs.
 % \begin{macrocode}
-\newcommand{\rrD}{\textbf{\textsf{D}}}
+\newcommand{\rrD}{\@rr{D}}
 %%
 \newcommand{\SquareD}{%
 \begin{tikzpicture}[scale=0.5]
@@ -4669,15 +6056,16 @@
 \draw [thick, ->]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhD}{\raisebox{-0.333\height}{\SquareD}\,}
+\newcommand{\rrhD}{\raisebox{-0.333\height}{\@tlen\SquareD\@tlen}}
 %%
 \newcommand{\RubikD}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareD\\
-\rrD
+\rrD%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikD}{\rrD\,\rrhD}
 %    \end{macrocode}
 %    \end{macro}
@@ -4696,7 +6084,7 @@
 %  \begin{macro}{\textRubikDp}
 %  These commands  all draw forms which denote the Dp rotation.
 % \begin{macrocode}
-\newcommand{\rrDp}{\textbf{\textsf{D}$^\prime$}}
+\newcommand{\rrDp}{\@rrp{D}}
 %%
 \newcommand{\SquareDp}{%
 \begin{tikzpicture}[scale=0.5]
@@ -4706,15 +6094,16 @@
 \draw [thick, <-] (\@sb,\@sd)   -- (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhDp}{\raisebox{-0.333\height}{\SquareDp}\,}
+\newcommand{\rrhDp}{\raisebox{-0.333\height}{\@tlen\SquareDp\@tlen}}
 %%
 \newcommand{\RubikDp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareDp\\
-\rrDp
+\rrDp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikDp}{\rrDp\,\rrhDp}
 %    \end{macrocode}
 %    \end{macro}
@@ -4733,7 +6122,7 @@
 %  \begin{macro}{\textRubikDw}
 %  These commands  all draw forms which denote the Dw rotation.
 % \begin{macrocode}
-\newcommand{\rrDw}{\textbf{\textsf{D\footnotesize{w}}}}
+\newcommand{\rrDw}{\@rrw{D}}
 %%
 \newcommand{\SquareDw}{%
 \begin{tikzpicture}[scale=0.5]
@@ -4743,15 +6132,16 @@
 \draw [thick, ->] (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhDw}{\raisebox{-0.333\height}{\SquareDw}\,}
+\newcommand{\rrhDw}{\raisebox{-0.333\height}{\@tlen\SquareDw\@tlen}}
 %%
 \newcommand{\RubikDw}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareDw\\
-\rrDw
+\rrDw%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikDw}{\rrDw\,\rrhDw}
 %    \end{macrocode}
 %    \end{macro}
@@ -4770,7 +6160,7 @@
 %  \begin{macro}{\textRubikDwp}
 %  These commands  all draw forms which denote the Dwp rotation.
 % \begin{macrocode}
-\newcommand{\rrDwp}{\textbf{\textsf{D\footnotesize{w}}$^\prime$}}
+\newcommand{\rrDwp}{\@rrwp{D}}
 %%
 \newcommand{\SquareDwp}{%
 \begin{tikzpicture}[scale=0.5]
@@ -4780,15 +6170,16 @@
 \draw [thick, <-] (\@sb,\@sd)   -- (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhDwp}{\raisebox{-0.333\height}{\SquareDwp}\,}
+\newcommand{\rrhDwp}{\raisebox{-0.333\height}{\@tlen\SquareDwp\@tlen}}
 %%
 \newcommand{\RubikDwp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareDwp\\
-\rrDwp
+\rrDwp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikDwp}{\rrDwp\,\rrhDwp}
 %    \end{macrocode}
 %    \end{macro}
@@ -4817,15 +6208,16 @@
 \draw [thick, ->]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhDs}{\raisebox{-0.333\height}{\SquareDs}\,}
+\newcommand{\rrhDs}{\raisebox{-0.333\height}{\@tlen\SquareDs\@tlen}}
 %%
 \newcommand{\RubikDs}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareDs\\
-\rrDs
+\rrDs%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikDs}{\rrDs\,\rrhDs}
 %    \end{macrocode}
 %    \end{macro}
@@ -4854,15 +6246,16 @@
 \draw [thick, <-]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhDsp}{\raisebox{-0.333\height}{\SquareDsp}\,}
+\newcommand{\rrhDsp}{\raisebox{-0.333\height}{\@tlen\SquareDsp\@tlen}}
 %%
 \newcommand{\RubikDsp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareDsp\\
-\rrDsp
+\rrDsp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikDsp}{\rrDsp\,\rrhDsp}
 %    \end{macrocode}
 %    \end{macro}
@@ -4891,15 +6284,16 @@
 \draw [thick, ->]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhDa}{\raisebox{-0.333\height}{\SquareDa}\,}
+\newcommand{\rrhDa}{\raisebox{-0.333\height}{\@tlen\SquareDa\@tlen}}
 %%
 \newcommand{\RubikDa}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareDa\\
-\rrDa
+\rrDa%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikDa}{\rrDa\,\rrhDa}
 %    \end{macrocode}
 %    \end{macro}
@@ -4928,15 +6322,16 @@
 \draw [thick, <-]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhDap}{\raisebox{-0.333\height}{\SquareDap}\,}
+\newcommand{\rrhDap}{\raisebox{-0.333\height}{\@tlen\SquareDap\@tlen}}
 %%
 \newcommand{\RubikDap}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareDap\\
-\rrDap
+\rrDap%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikDap}{\rrDap\,\rrhDap}
 %    \end{macrocode}
 %    \end{macro}
@@ -4955,7 +6350,7 @@
 %  \begin{macro}{\textRubikE}
 %  These commands  all draw forms which denote the E rotation.
 % \begin{macrocode}
-\newcommand{\rrE}{\textbf{\textsf{E}}}
+\newcommand{\rrE}{\@rr{E}}
 %%
 \newcommand{\SquareE}{%
 \begin{tikzpicture}[scale=0.5]
@@ -4965,15 +6360,16 @@
 \draw [thick]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhE}{\raisebox{-0.333\height}{\SquareE}\,}
+\newcommand{\rrhE}{\raisebox{-0.333\height}{\@tlen\SquareE\@tlen}}
 %%
 \newcommand{\RubikE}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareE\\
-\rrE
+\rrE%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikE}{\rrE\,\rrhE}
 %    \end{macrocode}
 %    \end{macro}
@@ -4992,7 +6388,7 @@
 %  \begin{macro}{\textRubikEp}
 %  These commands  all draw forms which denote the Ep rotation.
 % \begin{macrocode}
-\newcommand{\rrEp}{\textbf{\textsf{E}$^\prime$}}
+\newcommand{\rrEp}{\@rrp{E}}
 %%
 \newcommand{\SquareEp}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5002,15 +6398,16 @@
 \draw [thick]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhEp}{\raisebox{-0.333\height}{\SquareEp}\,}
+\newcommand{\rrhEp}{\raisebox{-0.333\height}{\@tlen\SquareEp\@tlen}}
 %%
 \newcommand{\RubikEp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareEp\\
-\rrEp
+\rrEp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikEp}{\rrEp\,\rrhEp}
 %    \end{macrocode}
 %    \end{macro}
@@ -5029,7 +6426,7 @@
 %  \begin{macro}{\textRubikF}
 %  These commands  all draw forms which denote the F rotation.
 %  \begin{macrocode}
-\newcommand{\rrF}{\textbf{\textsf{F}}}
+\newcommand{\rrF}{\@rr{F}}
 %%
 \newcommand{\SquareF}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5037,15 +6434,16 @@
 \draw [thick, <-] (\@scx, \@scy) arc[radius=0.35, start angle=-60, delta angle=290];
 \end{tikzpicture}%
 }
-\newcommand{\rrhF}{\raisebox{-0.333\height}{\SquareF}\,}
+\newcommand{\rrhF}{\raisebox{-0.333\height}{\@tlen\SquareF\@tlen}}
 %%
 \newcommand{\RubikF}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareF\\
-\rrF
+\rrF%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikF}{\rrF\,\rrhF}
 %    \end{macrocode}
 %    \end{macro}
@@ -5064,7 +6462,7 @@
 %  \begin{macro}{\textRubikFp}
 %  These commands  all draw forms which denote the Fp rotation.
 % \begin{macrocode}
-\newcommand{\rrFp}{\textbf{\textsf{F}$^\prime$}}
+\newcommand{\rrFp}{\@rrp{F}}
 %%
 \newcommand{\SquareFp}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5072,15 +6470,16 @@
 \draw [thick, ->] (\@scx, \@scy) arc[radius=0.35, start angle=-60, delta angle=290];
 \end{tikzpicture}%
 }
-\newcommand{\rrhFp}{\raisebox{-0.333\height}{\SquareFp}\,}
+\newcommand{\rrhFp}{\raisebox{-0.333\height}{\@tlen\SquareFp\@tlen}}
 %%
 \newcommand{\RubikFp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareFp\\
-\rrFp
+\rrFp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikFp}{\rrFp\,\rrhFp}
 %    \end{macrocode}
 %    \end{macro}
@@ -5099,7 +6498,7 @@
 %  \begin{macro}{\textRubikFw}
 %  These commands  all draw forms which denote the Fw rotation.
 % \begin{macrocode}
-\newcommand{\rrFw}{\textbf{\textsf{F\footnotesize{w}}}}
+\newcommand{\rrFw}{\@rrw{F}}
 %%
 \newcommand{\SquareFw}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5109,15 +6508,16 @@
 %\node (squareLab) at (0.5,0.5)  {$o$};
 \end{tikzpicture}%
 }
-\newcommand{\rrhFw}{\raisebox{-0.333\height}{\SquareFw}\,}
+\newcommand{\rrhFw}{\raisebox{-0.333\height}{\@tlen\SquareFw\@tlen}}
 %%
 \newcommand{\RubikFw}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareFw\\
-\rrFw
+\rrFw%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikFw}{\rrFw\,\rrhFw}
 %    \end{macrocode}
 %    \end{macro}
@@ -5136,7 +6536,7 @@
 %  \begin{macro}{\textRubikFwp}
 %  These commands  all draw forms which denote the Fwp rotation.
 % \begin{macrocode}
-\newcommand{\rrFwp}{\textbf{\textsf{F\footnotesize{w}}$^\prime$}}
+\newcommand{\rrFwp}{\@rrwp{F}}
 %%
 \newcommand{\SquareFwp}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5145,15 +6545,16 @@
 \draw [thick] (\@sqcx,\@sqcy) arc[radius=0.1, start angle=-60, delta angle=360];
 \end{tikzpicture}%
 }
-\newcommand{\rrhFwp}{\raisebox{-0.333\height}{\SquareFwp}\,}
+\newcommand{\rrhFwp}{\raisebox{-0.333\height}{\@tlen\SquareFwp\@tlen}}
 %%
 \newcommand{\RubikFwp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareFwp\\
-\rrFwp
+\rrFwp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikFwp}{\rrFwp\,\rrhFwp}
 %%
 %    \end{macrocode}
@@ -5179,10 +6580,10 @@
 %  Not visible from the front.
 % \begin{macrocode}
 \newcommand{\rrFs}{\@rrs{F}}
-\newcommand{\SquareFs}{\@SquareLetter{\rrFs}} 
-\newcommand{\rrhFs}{\raisebox{-0.25mm}{\SquareFs}\,}
-\newcommand{\RubikFs}{\raisebox{\@hRubik}{\SquareFs}\,}
-\newcommand{\textRubikFs}{\rrhFs\,}
+\newcommand{\SquareFs}{\@tlen\@SquareLetter{\rrFs}\@tlen} 
+\newcommand{\rrhFs}{\raisebox{-0.25mm}{\SquareFs}}
+\newcommand{\RubikFs}{\raisebox{\@hRubik}{\SquareFs}}
+\newcommand{\textRubikFs}{\rrhFs}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -5205,10 +6606,10 @@
 %  Not visible from the front.
 % \begin{macrocode}
 \newcommand{\rrFsp}{\@rrsp{F}}
-\newcommand{\SquareFsp}{\@SquareLetter{\rrFsp}}
-\newcommand{\rrhFsp}{\raisebox{-0.25mm}{\SquareFsp}\,}
-\newcommand{\RubikFsp}{\raisebox{\@hRubik}{\SquareFsp}\,}
-\newcommand{\textRubikFsp}{\rrhFsp\,}
+\newcommand{\SquareFsp}{\@tlen\@SquareLetter{\rrFsp}\@tlen}
+\newcommand{\rrhFsp}{\raisebox{-0.25mm}{\SquareFsp}}
+\newcommand{\RubikFsp}{\raisebox{\@hRubik}{\SquareFsp}}
+\newcommand{\textRubikFsp}{\rrhFsp}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -5231,10 +6632,10 @@
 %  Not visible from the front.
 % \begin{macrocode}
 \newcommand{\rrFa}{\@rra{F}}
-\newcommand{\SquareFa}{\@SquareLetter{\rrFa}}
-\newcommand{\rrhFa}{\raisebox{-0.25mm}{\SquareFa}\,}
-\newcommand{\RubikFa}{\raisebox{\@hRubik}{\SquareFa}\,}
-\newcommand{\textRubikFa}{\rrhFa\,}
+\newcommand{\SquareFa}{\@tlen\@SquareLetter{\rrFa}\@tlen}
+\newcommand{\rrhFa}{\raisebox{-0.25mm}{\SquareFa}}
+\newcommand{\RubikFa}{\raisebox{\@hRubik}{\SquareFa}}
+\newcommand{\textRubikFa}{\rrhFa}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -5257,10 +6658,10 @@
 %  Not visible from the front.
 % \begin{macrocode}
 \newcommand{\rrFap}{\@rrap{F}}
-\newcommand{\SquareFap}{\@SquareLetter{\rrFap}}
-\newcommand{\rrhFap}{\raisebox{-0.25mm}{\SquareFap}\,}
-\newcommand{\RubikFap}{\raisebox{\@hRubik}{\SquareFap}\,}
-\newcommand{\textRubikFap}{\rrhFap\,}
+\newcommand{\SquareFap}{\@tlen\@SquareLetter{\rrFap}\@tlen}
+\newcommand{\rrhFap}{\raisebox{-0.25mm}{\SquareFap}}
+\newcommand{\RubikFap}{\raisebox{\@hRubik}{\SquareFap}}
+\newcommand{\textRubikFap}{\rrhFap}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -5277,7 +6678,7 @@
 %  \begin{macro}{\textRubikL}
 %  These commands  all draw forms which denote the L rotation.
 % \begin{macrocode}
-\newcommand{\rrL}{\textbf{\textsf{L}}}
+\newcommand{\rrL}{\@rr{L}}
 %%
 \newcommand{\SquareL}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5287,15 +6688,16 @@
 \draw [thick] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhL}{\raisebox{-0.333\height}{\SquareL}\,}
+\newcommand{\rrhL}{\raisebox{-0.333\height}{\@tlen\SquareL\@tlen}}
 %%
 \newcommand{\RubikL}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareL\\
-\rrL
+\rrL%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikL}{\rrL\,\rrhL}
 %    \end{macrocode}
 %    \end{macro}
@@ -5314,7 +6716,7 @@
 %  \begin{macro}{\textRubikLp}
 %  These commands  all draw forms which denote the Lp rotation.
 % \begin{macrocode}
-\newcommand{\rrLp}{\textbf{\textsf{L}$^\prime$}}
+\newcommand{\rrLp}{\@rrp{L}}
 %%
 \newcommand{\SquareLp}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5324,15 +6726,16 @@
 \draw [thick] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhLp}{\raisebox{-0.333\height}{\SquareLp}\,}
+\newcommand{\rrhLp}{\raisebox{-0.333\height}{\@tlen\SquareLp\@tlen}}
 %%
 \newcommand{\RubikLp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareLp\\
-\rrLp
+\rrLp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikLp}{\rrLp\,\rrhLp}
 %    \end{macrocode}
 %    \end{macro}
@@ -5351,7 +6754,7 @@
 %  \begin{macro}{\textRubikLw}
 %  These commands  all draw forms which denote the Lw rotation.
 % \begin{macrocode}
-\newcommand{\rrLw}{\textbf{\textsf{L\footnotesize{w}}}}
+\newcommand{\rrLw}{\@rrw{L}}
 %%
 \newcommand{\SquareLw}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5361,15 +6764,16 @@
 \draw [thick] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhLw}{\raisebox{-0.333\height}{\SquareLw}\,}
+\newcommand{\rrhLw}{\raisebox{-0.333\height}{\@tlen\SquareLw\@tlen}}
 %%
 \newcommand{\RubikLw}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareLw\\
-\rrLw
+\rrLw%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikLw}{\rrLw\,\rrhLw}
 %    \end{macrocode}
 %    \end{macro}
@@ -5388,7 +6792,7 @@
 %  \begin{macro}{\textRubikLwp}
 %  These commands  all draw forms which denote the Lwp rotation.
 % \begin{macrocode}
-\newcommand{\rrLwp}{\textbf{\textsf{L\footnotesize{w}}$^\prime$}}
+\newcommand{\rrLwp}{\@rrwp{L}}
 %%
 \newcommand{\SquareLwp}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5398,15 +6802,16 @@
 \draw [thick] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhLwp}{\raisebox{-0.333\height}{\SquareLwp}\,}
+\newcommand{\rrhLwp}{\raisebox{-0.333\height}{\@tlen\SquareLwp\@tlen}}
 %%
 \newcommand{\RubikLwp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareLwp\\
-\rrLwp
+\rrLwp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikLwp}{\rrLwp\,\rrhLwp}
 %    \end{macrocode}
 %    \end{macro}
@@ -5435,15 +6840,16 @@
 \draw [thick, <-] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhLs}{\raisebox{-0.333\height}{\SquareLs}\,}
+\newcommand{\rrhLs}{\raisebox{-0.333\height}{\@tlen\SquareLs\@tlen}}
 %%
 \newcommand{\RubikLs}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareLs\\
-\rrLs
+\rrLs%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikLs}{\rrLs\,\rrhLs}
 %    \end{macrocode}
 %    \end{macro}
@@ -5472,15 +6878,16 @@
 \draw [thick, ->] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhLsp}{\raisebox{-0.333\height}{\SquareLsp}\,}
+\newcommand{\rrhLsp}{\raisebox{-0.333\height}{\@tlen\SquareLsp\@tlen}}
 %%
 \newcommand{\RubikLsp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareLsp\\
-\rrLsp
+\rrLsp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikLsp}{\rrLsp\,\rrhLsp}
 %    \end{macrocode}
 %    \end{macro}
@@ -5509,15 +6916,16 @@
 \draw [thick, ->] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhLa}{\raisebox{-0.333\height}{\SquareLa}\,}
+\newcommand{\rrhLa}{\raisebox{-0.333\height}{\@tlen\SquareLa\@tlen}}
 %%
 \newcommand{\RubikLa}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareLa\\
-\rrLa
+\rrLa%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikLa}{\rrLa\,\rrhLa}
 %    \end{macrocode}
 %    \end{macro}
@@ -5546,15 +6954,16 @@
 \draw [thick, <-] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhLap}{\raisebox{-0.333\height}{\SquareLap}\,}
+\newcommand{\rrhLap}{\raisebox{-0.333\height}{\@tlen\SquareLap\@tlen}}
 %%
 \newcommand{\RubikLap}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareLap\\
-\rrLap
+\rrLap%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikLap}{\rrLap\,\rrhLap}
 %    \end{macrocode}
 %    \end{macro}
@@ -5573,7 +6982,7 @@
 %  \begin{macro}{\textRubikM}
 %  These commands  all draw forms which denote the M rotation.
 % \begin{macrocode}
-\newcommand{\rrM}{\textbf{\textsf{M}}}
+\newcommand{\rrM}{\@rr{M}}
 %%
 \newcommand{\SquareM}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5583,15 +6992,16 @@
 \draw [thick] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhM}{\raisebox{-0.333\height}{\SquareM}\,}
+\newcommand{\rrhM}{\raisebox{-0.333\height}{\@tlen\SquareM\@tlen}}
 %%
 \newcommand{\RubikM}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareM\\
-\rrM
+\rrM%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikM}{\rrM\,\rrhM}
 %    \end{macrocode}
 %    \end{macro}
@@ -5610,7 +7020,7 @@
 %  \begin{macro}{\textRubikMp}
 %  These commands  all draw forms which denote the Mp rotation.
 % \begin{macrocode}
-\newcommand{\rrMp}{\textbf{\textsf{M}$^\prime$}}
+\newcommand{\rrMp}{\@rrp{M}}
 %%
 \newcommand{\SquareMp}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5620,15 +7030,16 @@
 \draw [thick] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhMp}{\raisebox{-0.333\height}{\SquareMp}\,}
+\newcommand{\rrhMp}{\raisebox{-0.333\height}{\@tlen\SquareMp\@tlen}}
 %%
 \newcommand{\RubikMp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareMp\\
-\rrMp
+\rrMp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikMp}{\rrMp\,\rrhMp}
 %    \end{macrocode}
 %    \end{macro}
@@ -5647,7 +7058,7 @@
 %  \begin{macro}{\textRubikR}
 %  These commands  all draw forms which denote the R rotation.
 % \begin{macrocode}
-\newcommand{\rrR}{\textbf{\textsf{R}}}
+\newcommand{\rrR}{\@rr{R}}
 %%
 \newcommand{\SquareR}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5658,15 +7069,16 @@
 \draw [thick, ->] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhR}{\raisebox{-0.333\height}{\SquareR}\,}
+\newcommand{\rrhR}{\raisebox{-0.333\height}{\@tlen\SquareR\@tlen}}
 %%
 \newcommand{\RubikR}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareR\\
-\rrR
+\rrR%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikR}{\rrR\,\rrhR}
 %    \end{macrocode}
 %    \end{macro}
@@ -5685,7 +7097,7 @@
 %  \begin{macro}{\textRubikRp}
 %  These commands  all draw forms which denote the Rp rotation.
 % \begin{macrocode}
-\newcommand{\rrRp}{\textbf{\textsf{R}$^\prime$}}
+\newcommand{\rrRp}{\@rrp{R}}
 %%
 \newcommand{\SquareRp}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5695,15 +7107,16 @@
 \draw [thick, <-] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhRp}{\raisebox{-0.333\height}{\SquareRp}\,}
+\newcommand{\rrhRp}{\raisebox{-0.333\height}{\@tlen\SquareRp\@tlen}}
 %%
 \newcommand{\RubikRp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareRp\\
-\rrRp
+\rrRp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikRp}{\rrRp\,\rrhRp}
 %    \end{macrocode}
 %    \end{macro}
@@ -5722,7 +7135,7 @@
 %  \begin{macro}{\textRubikRw}
 %  These commands  all draw forms which denote the Rw rotation.
 % \begin{macrocode}
-\newcommand{\rrRw}{\textbf{\textsf{R\footnotesize{w}}}}
+\newcommand{\rrRw}{\@rrw{R}}
 %%
 \newcommand{\SquareRw}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5732,15 +7145,16 @@
 \draw [thick, ->] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhRw}{\raisebox{-0.333\height}{\SquareRw}\,}
+\newcommand{\rrhRw}{\raisebox{-0.333\height}{\@tlen\SquareRw\@tlen}}
 %%
 \newcommand{\RubikRw}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareRw\\
-\rrRw
+\rrRw%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikRw}{\rrRw\,\rrhRw}
 %    \end{macrocode}
 %    \end{macro}
@@ -5759,7 +7173,7 @@
 %  \begin{macro}{\textRubikRwp}
 %  These commands  all draw forms which denote the Rwp rotation.
 % \begin{macrocode}
-\newcommand{\rrRwp}{\textbf{\textsf{R\footnotesize{w}}$^\prime$}}
+\newcommand{\rrRwp}{\@rrwp{R}}
 %%
 \newcommand{\SquareRwp}{%
 \begin{tikzpicture}[scale=0.5]
@@ -5769,15 +7183,16 @@
 \draw [thick, <-] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhRwp}{\raisebox{-0.333\height}{\SquareRwp}\,}
+\newcommand{\rrhRwp}{\raisebox{-0.333\height}{\@tlen\SquareRwp\@tlen}}
 %%
 \newcommand{\RubikRwp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareRwp\\
-\rrRwp
+\rrRwp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikRwp}{\rrRwp\,\rrhRwp}
 %    \end{macrocode}
 %    \end{macro}
@@ -5806,15 +7221,16 @@
 \draw [thick,->] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhRs}{\raisebox{-0.333\height}{\SquareRs}\,}
+\newcommand{\rrhRs}{\raisebox{-0.333\height}{\@tlen\SquareRs\@tlen}}
 %%
 \newcommand{\RubikRs}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareRs\\
-\rrRs
+\rrRs%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikRs}{\rrRs\,\rrhRs}
 %    \end{macrocode}
 %    \end{macro}
@@ -5843,15 +7259,16 @@
 \draw [thick,<-] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhRsp}{\raisebox{-0.333\height}{\SquareRsp}\,}
+\newcommand{\rrhRsp}{\raisebox{-0.333\height}{\@tlen\SquareRsp\@tlen}}
 %%
 \newcommand{\RubikRsp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareRsp\\
-\rrRsp
+\rrRsp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikRsp}{\rrRsp\,\rrhRsp}
 %    \end{macrocode}
 %    \end{macro}
@@ -5880,15 +7297,16 @@
 \draw [thick,->] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhRa}{\raisebox{-0.333\height}{\SquareRa}\,}
+\newcommand{\rrhRa}{\raisebox{-0.333\height}{\@tlen\SquareRa\@tlen}}
 %%
 \newcommand{\RubikRa}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareRa\\
-\rrRa
+\rrRa%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikRa}{\rrRa\,\rrhRa}
 %    \end{macrocode}
 %    \end{macro}
@@ -5917,15 +7335,16 @@
 \draw [thick,<-] (\@sddd, \@sb) -- (\@sddd, \@sbh);
 \end{tikzpicture}%
 }
-\newcommand{\rrhRap}{\raisebox{-0.333\height}{\SquareRap}\,}
+\newcommand{\rrhRap}{\raisebox{-0.333\height}{\@tlen\SquareRap\@tlen}}
 %%
 \newcommand{\RubikRap}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareRap\\
-\rrRap
+\rrRap%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikRap}{\rrRap\,\rrhRap}
 %    \end{macrocode}
 %    \end{macro}
@@ -5946,10 +7365,10 @@
 % Not visible from the front.
 % \begin{macrocode}
 \newcommand{\rrS}{\@rr{S}}
-\newcommand{\SquareS}{\@SquareLetter{\rrS}}
-\newcommand{\rrhS}{\raisebox{-0.25mm}{\SquareS}\,}
-\newcommand{\RubikS}{\raisebox{\@hRubik}{\SquareS}\,}
-\newcommand{\textRubikS}{\rrhS\,}
+\newcommand{\SquareS}{\@tlen\@SquareLetter{\rrS}\@tlen}
+\newcommand{\rrhS}{\raisebox{-0.25mm}{\SquareS}}
+\newcommand{\RubikS}{\raisebox{\@hRubik}{\SquareS}}
+\newcommand{\textRubikS}{\rrhS}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -5969,10 +7388,10 @@
 % Not visible from the front.
 % \begin{macrocode}
 \newcommand{\rrSp}{\@rrp{S}}
-\newcommand{\SquareSp}{\@SquareLetter{\rrSp}}
-\newcommand{\rrhSp}{\raisebox{-0.25mm}{\SquareSp}\,}
-\newcommand{\RubikSp}{\raisebox{\@hRubik}{\SquareSp}\,}
-\newcommand{\textRubikSp}{\rrhSp\,}
+\newcommand{\SquareSp}{\@tlen\@SquareLetter{\rrSp}\@tlen}
+\newcommand{\rrhSp}{\raisebox{-0.25mm}{\SquareSp}}
+\newcommand{\RubikSp}{\raisebox{\@hRubik}{\SquareSp}}
+\newcommand{\textRubikSp}{\rrhSp}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -5988,18 +7407,19 @@
 %  \begin{macro}{\RubikSu}
 %  \begin{macro}{\textRubikSu}
 %  These commands  draw forms of the Singmaster Su slice rotation.
-%  We also need to finetune the spacing 
+%  We also need to fine-tune the spacing 
 %  between these `slice' hieroglyphs (especially Fs  and Bs).
 % \begin{macrocode}
-\newcommand{\rrSu}{\textbf{\textsf{S\footnotesize{u}}}}
+\newcommand{\rrSu}{\@rru{S}}
 \newcommand{\rrhSu}{\rrhEp}%
 \newcommand{\RubikSu}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareEp\\
-\rrSu
+\rrSu%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikSu}{\rrSu\,\rrhEp}
 %    \end{macrocode}
 %    \end{macro}
@@ -6015,18 +7435,19 @@
 %  \begin{macro}{\RubikSup}
 %  \begin{macro}{\textRubikSup}
 %  These commands  draw forms of the Singmaster Sup slice rotation.
-%  We also need to finetune the spacing 
+%  We also need to fine-tune the spacing 
 %  between these `slice' hieroglyphs (especially Fs  and Bs).
 % \begin{macrocode}
-\newcommand{\rrSup}{\textbf{\textsf{S\footnotesize{u}}$^\prime$}}
+\newcommand{\rrSup}{\@rrup{S}}
 \newcommand{\rrhSup}{\rrhE}%
 \newcommand{\RubikSup}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareE\\
-\rrSup
+\rrSup%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikSup}{\rrSup\,\rrhE}
 %    \end{macrocode}
 %    \end{macro}
@@ -6043,15 +7464,16 @@
 %  \begin{macro}{\textRubikSd}
 %  These commands  draw forms of the Singmaster Sd slice rotation.
 % \begin{macrocode}
-\newcommand{\rrSd}{\textbf{\textsf{S\footnotesize{d}}}}
+\newcommand{\rrSd}{\@rrd{S}}
 \newcommand{\rrhSd}{\rrhE}%
 \newcommand{\RubikSd}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareE\\
-\rrSd
+\rrSd%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikSd}{\rrSd\,\rrhE}
 %    \end{macrocode}
 %    \end{macro}
@@ -6068,15 +7490,16 @@
 %  \begin{macro}{\textRubikSdp}
 %  These commands  draw forms of the Singmaster Sdp slice rotation.
 % \begin{macrocode}
-\newcommand{\rrSdp}{\textbf{\textsf{S\footnotesize{d}}$^\prime$}}
+\newcommand{\rrSdp}{\@rrdp{S}}
 \newcommand{\rrhSdp}{\rrhEp}%
 \newcommand{\RubikSdp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareEp\\
-\rrSdp
+\rrSdp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikSdp}{\rrSdp\,\rrhEp}
 %    \end{macrocode}
 %    \end{macro}
@@ -6093,15 +7516,16 @@
 %  \begin{macro}{\textRubikSl}
 %  These commands  draw forms of the Singmaster Sl slice rotation.
 % \begin{macrocode}
-\newcommand{\rrSl}{\textbf{\textsf{S\footnotesize{l}}}}
+\newcommand{\rrSl}{\@rrl{S}}
 \newcommand{\rrhSl}{\rrhM}%
 \newcommand{\RubikSl}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareM\\
-\rrSl
+\rrSl%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikSl}{\rrSl\,\rrhM}
 %    \end{macrocode}
 %    \end{macro}
@@ -6118,15 +7542,16 @@
 %  \begin{macro}{\textRubikSlp}
 %  These commands  draw forms of the Singmaster Slp slice rotation.
 % \begin{macrocode}
-\newcommand{\rrSlp}{\textbf{\textsf{S\footnotesize{l}}$^\prime$}}
+\newcommand{\rrSlp}{\@rrlp{S}}
 \newcommand{\rrhSlp}{\rrhMp}%
 \newcommand{\RubikSlp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareMp\\
-\rrSlp
+\rrSlp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikSlp}{\rrSlp\,\rrhMp}
 %    \end{macrocode}
 %    \end{macro}
@@ -6143,15 +7568,16 @@
 %  \begin{macro}{\textRubikSr}
 %  These commands  draw forms of the Singmaster Sr slice rotation.
 % \begin{macrocode}
-\newcommand{\rrSr}{\textbf{\textsf{S\footnotesize{r}}}}
+\newcommand{\rrSr}{\@rrr{S}}
 \newcommand{\rrhSr}{\rrhMp}%
 \newcommand{\RubikSr}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareMp\\
-\rrSr
+\rrSr%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikSr}{\rrSr\,\rrhMp}
 %    \end{macrocode}
 %    \end{macro}
@@ -6168,15 +7594,16 @@
 %  \begin{macro}{\textRubikSrp}
 %  These commands  draw forms of the Singmaster Srp slice rotation.
 % \begin{macrocode}
-\newcommand{\rrSrp}{\textbf{\textsf{S\footnotesize{r}}$^\prime$}}
+\newcommand{\rrSrp}{\@rrrp{S}}
 \newcommand{\rrhSrp}{\rrhM}%
 \newcommand{\RubikSrp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareM\\
-\rrSrp
+\rrSrp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikSrp}{\rrSrp\,\rrhM}
 %    \end{macrocode}
 %    \end{macro}
@@ -6199,11 +7626,11 @@
 %  bounded by \{\} so no need to reset to defaults.
 % Not visible from the front.
 % \begin{macrocode}
-\newcommand{\rrSf}{\textbf{\textsf{S\footnotesize{f}}}}
-\newcommand{\SquareSf}{\@SquareLetter{\rrSf}}
-\newcommand{\rrhSf}{\raisebox{-0.25mm}{\SquareSf}\,}
-\newcommand{\RubikSf}{\raisebox{\@hRubik}{\SquareSf}\,}
-\newcommand{\textRubikSf}{\rrhSf\,}
+\newcommand{\rrSf}{\@rrf{S}}
+\newcommand{\SquareSf}{\@tlen\@SquareLetter{\rrSf}\@tlen}
+\newcommand{\rrhSf}{\raisebox{-0.25mm}{\SquareSf}}
+\newcommand{\RubikSf}{\raisebox{\@hRubik}{\SquareSf}}
+\newcommand{\textRubikSf}{\rrhSf}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -6225,11 +7652,11 @@
 %  bounded by \{\} so no need to reset to defaults.
 % Not visible from the front.
 % \begin{macrocode}
-\newcommand{\rrSfp}{\textbf{\textsf{S\footnotesize{f}}$^\prime$}}
-\newcommand{\SquareSfp}{\@SquareLetter{\rrSfp}}
-\newcommand{\rrhSfp}{\raisebox{-0.25mm}{\SquareSfp}\,}
-\newcommand{\RubikSfp}{\raisebox{\@hRubik}{\SquareSfp}\,}
-\newcommand{\textRubikSfp}{\rrhSfp\,}
+\newcommand{\rrSfp}{\@rrfp{S}}
+\newcommand{\SquareSfp}{\@tlen\@SquareLetter{\rrSfp}\@tlen}
+\newcommand{\rrhSfp}{\raisebox{-0.25mm}{\SquareSfp}}
+\newcommand{\RubikSfp}{\raisebox{\@hRubik}{\SquareSfp}}
+\newcommand{\textRubikSfp}{\rrhSfp}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -6251,11 +7678,11 @@
 %  bounded by \{\} so no need to reset to defaults.
 % Not visible from the front.
 % \begin{macrocode}
-\newcommand{\rrSb}{\textbf{\textsf{S\footnotesize{b}}}}
-\newcommand{\SquareSb}{\@SquareLetter{\rrSb}}
-\newcommand{\rrhSb}{\raisebox{-0.25mm}{\SquareSb}\,}
-\newcommand{\RubikSb}{\raisebox{\@hRubik}{\SquareSb}\,}
-\newcommand{\textRubikSb}{\rrhSb\,}
+\newcommand{\rrSb}{\@rrb{S}}
+\newcommand{\SquareSb}{\@tlen\@SquareLetter{\rrSb}\@tlen}
+\newcommand{\rrhSb}{\raisebox{-0.25mm}{\SquareSb}}
+\newcommand{\RubikSb}{\raisebox{\@hRubik}{\SquareSb}}
+\newcommand{\textRubikSb}{\rrhSb}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -6277,11 +7704,11 @@
 %  bounded by \{\} so no need to reset to defaults.
 % Not visible from th front.
 % \begin{macrocode}
-\newcommand{\rrSbp}{\textbf{\textsf{S\footnotesize{b}}$^\prime$}}
-\newcommand{\SquareSbp}{\@SquareLetter{\rrSbp}}
-\newcommand{\rrhSbp}{\raisebox{-0.25mm}{\SquareSbp}\,}
-\newcommand{\RubikSbp}{\raisebox{\@hRubik}{\SquareSbp}\,}
-\newcommand{\textRubikSbp}{\rrhSbp\,}
+\newcommand{\rrSbp}{\@rrbp{S}}
+\newcommand{\SquareSbp}{\@tlen\@SquareLetter{\rrSbp}\@tlen}
+\newcommand{\rrhSbp}{\raisebox{-0.25mm}{\SquareSbp}}
+\newcommand{\RubikSbp}{\raisebox{\@hRubik}{\SquareSbp}}
+\newcommand{\textRubikSbp}{\rrhSbp}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -6298,7 +7725,7 @@
 %  \begin{macro}{\textRubikU}
 %  These commands  all draw forms which denote the U rotation.
 % \begin{macrocode}
-\newcommand{\rrU}{\textbf{\textsf{U}}}
+\newcommand{\rrU}{\@rr{U}}
 %%
 \newcommand{\SquareU}{%
 \begin{tikzpicture}[scale=0.5]
@@ -6308,15 +7735,16 @@
 \draw [thick]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhU}{\raisebox{-0.333\height}{\SquareU}\,}
+\newcommand{\rrhU}{\raisebox{-0.333\height}{\@tlen\SquareU\@tlen}}
 %%
 \newcommand{\RubikU}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareU\\
-\rrU
+\rrU%
 \end{minipage}%%
-}
+}}
 \newcommand{\textRubikU}{\rrU\,\rrhU}
 %    \end{macrocode}
 %    \end{macro}
@@ -6335,7 +7763,7 @@
 %  \begin{macro}{\textRubikUw}
 %  These commands  all draw forms which denote the Uw rotation.
 % \begin{macrocode}
-\newcommand{\rrUw}{\textbf{\textsf{U\footnotesize{w}}}}
+\newcommand{\rrUw}{\@rrw{U}}
 %%
 \newcommand{\SquareUw}{%
 \begin{tikzpicture}[scale=0.5]
@@ -6346,15 +7774,16 @@
 \end{tikzpicture}%
 }
 %
-\newcommand{\rrhUw}{\raisebox{-0.333\height}{\SquareUw}\,}
+\newcommand{\rrhUw}{\raisebox{-0.333\height}{\@tlen\SquareUw\@tlen}}
 %%
 \newcommand{\RubikUw}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareUw\\
-\rrUw
+\rrUw%
 \end{minipage}%%
-}
+}}
 %%
 \newcommand{\textRubikUw}{\rrUw\,\rrhUw}
 %    \end{macrocode}
@@ -6374,7 +7803,7 @@
 %  \begin{macro}{\textRubikUp}
 %  These commands  all draw forms which denote the Up rotation.
 % \begin{macrocode}
-\newcommand{\rrUp}{\textbf{\textsf{U}$^\prime$}}
+\newcommand{\rrUp}{\@rrp{U}}
 %%
 \newcommand{\SquareUp}{%
 \begin{tikzpicture}[scale=0.5]
@@ -6384,15 +7813,16 @@
 \draw [thick]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhUp}{\raisebox{-0.333\height}{\SquareUp}\,}
+\newcommand{\rrhUp}{\raisebox{-0.333\height}{\@tlen\SquareUp\@tlen}}
 %%
 \newcommand{\RubikUp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareUp\\
-\rrUp
+\rrUp%
 \end{minipage}%%
-}
+}}
 \newcommand{\textRubikUp}{\rrUp\,\rrhUp}
 %    \end{macrocode}
 %    \end{macro}
@@ -6411,7 +7841,7 @@
 %  \begin{macro}{\textRubikUwp}
 %  These commands  all draw forms which denote the Uwp rotation.
 % \begin{macrocode}
-\newcommand{\rrUwp}{\textbf{\textsf{U\footnotesize{w}}$^\prime$}}
+\newcommand{\rrUwp}{\@rrwp{U}}
 %%
 \newcommand{\SquareUwp}{%
 \begin{tikzpicture}[scale=0.5]
@@ -6421,15 +7851,16 @@
 \draw [thick]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhUwp}{\raisebox{-0.333\height}{\SquareUwp}\,}
+\newcommand{\rrhUwp}{\raisebox{-0.333\height}{\@tlen\SquareUwp\@tlen}}
 %%
 \newcommand{\RubikUwp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareUwp\\
-\rrUwp
+\rrUwp%
 \end{minipage}%%
-}
+}}
 \newcommand{\textRubikUwp}{\rrUwp\,\rrhUwp}
 %    \end{macrocode}
 %    \end{macro}
@@ -6458,15 +7889,16 @@
 \draw [thick, <-]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhUs}{\raisebox{-0.333\height}{\SquareUs}\,}
+\newcommand{\rrhUs}{\raisebox{-0.333\height}{\@tlen\SquareUs\@tlen}}
 %%
 \newcommand{\RubikUs}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareUs\\
-\rrUs
+\rrUs%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikUs}{\rrUs\,\rrhUs}
 %    \end{macrocode}
 %    \end{macro}
@@ -6495,15 +7927,16 @@
 \draw [thick, ->]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhUsp}{\raisebox{-0.333\height}{\SquareUsp}\,}
+\newcommand{\rrhUsp}{\raisebox{-0.333\height}{\@tlen\SquareUsp\@tlen}}
 %%
 \newcommand{\RubikUsp}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareUsp\\
-\rrUsp
+\rrUsp%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikUsp}{\rrUsp\,\rrhUsp}
 %    \end{macrocode}
 %    \end{macro}
@@ -6532,15 +7965,16 @@
 \draw [thick, ->]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhUa}{\raisebox{-0.333\height}{\SquareUa}\,}
+\newcommand{\rrhUa}{\raisebox{-0.333\height}{\@tlen\SquareUa\@tlen}}
 %%
 \newcommand{\RubikUa}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareUa\\
-\rrUa
+\rrUa%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikUa}{\rrUa\,\rrhUa}
 %    \end{macrocode}
 %    \end{macro}
@@ -6569,15 +8003,16 @@
 \draw [thick, <-]     (\@sb,\@sd) --   (\@sbh, \@sd);
 \end{tikzpicture}%
 }
-\newcommand{\rrhUap}{\raisebox{-0.333\height}{\SquareUap}\,}
+\newcommand{\rrhUap}{\raisebox{-0.333\height}{\@tlen\SquareUap\@tlen}}
 %%
 \newcommand{\RubikUap}{%
+{\@rubikfont%
 \begin{minipage}{0.6cm}
-\centering
+\centering%
 \SquareUap\\
-\rrUap
+\rrUap%
 \end{minipage}%
-}
+}}
 \newcommand{\textRubikUap}{\rrUap\,\rrhUap}
 %    \end{macrocode}
 %    \end{macro}
@@ -6595,7 +8030,7 @@
 %  \begin{macro}{\Rubikx}
 %  These commands  all draw forms which denote the x rotation.
 % \begin{macrocode}
-\newcommand{\rrx}{\textbf{\textsf{x}}}
+\newcommand{\rrx}{\@rr{x}}
 \newcommand{\Rubikx}{\@xyzRubik{x}}
 \newcommand{\rrhx}{\@xyzh{x}}
 %    \end{macrocode}
@@ -6607,7 +8042,7 @@
 %  \begin{macro}{\Rubikxp}
 %  These commands  all draw forms which denote the xp rotation.
 % \begin{macrocode}
-\newcommand{\rrxp}{\textbf{\textsf{x}$^\prime$}}
+\newcommand{\rrxp}{\@rrp{x}}
 \newcommand{\Rubikxp}{\@xyzRubikp{x}}
 \newcommand{\rrhxp}{\@xyzhp{x}}
 %    \end{macrocode}
@@ -6623,7 +8058,7 @@
 %  \begin{macro}{\Rubiky}
 %  These commands  all draw forms which denote the y rotation.
 % \begin{macrocode}
-\newcommand{\rry}{\textbf{\textsf{y}}}
+\newcommand{\rry}{\@rr{y}}
 \newcommand{\Rubiky}{\@xyzRubik{y}}
 \newcommand{\rrhy}{\@xyzh{y}}
 %    \end{macrocode}
@@ -6635,7 +8070,7 @@
 %  \begin{macro}{\Rubikyp}
 %  These commands  all draw forms which denote the yp rotation.
 % \begin{macrocode}
-\newcommand{\rryp}{\textbf{\textsf{y}$^\prime$}}
+\newcommand{\rryp}{\@rrp{y}}
 \newcommand{\Rubikyp}{\@xyzRubikp{y}}
 \newcommand{\rrhyp}{\@xyzhp{y}}
 %    \end{macrocode}
@@ -6651,7 +8086,7 @@
 %  \begin{macro}{\Rubikz}
 %  These commands  all draw forms which denote the z rotation.
 % \begin{macrocode}
-\newcommand{\rrz}{\textbf{\textsf{z}}}
+\newcommand{\rrz}{\@rr{z}}
 \newcommand{\Rubikz}{\@xyzRubik{z}}
 \newcommand{\rrhz}{\@xyzh{z}}
 %    \end{macrocode}
@@ -6663,7 +8098,7 @@
 %  \begin{macro}{\Rubikzp}
 %  These commands  all draw forms which denote the zp rotation.
 % \begin{macrocode}
-\newcommand{\rrzp}{\textbf{\textsf{z}$^\prime$}}
+\newcommand{\rrzp}{\@rrp{z}}
 \newcommand{\Rubikzp}{\@xyzRubikp{z}}
 \newcommand{\rrhzp}{\@xyzhp{z}}
 %    \end{macrocode}
@@ -6679,7 +8114,7 @@
 %  \begin{macro}{\Rubiku}
 %  These commands  all draw forms which denote the u rotation.
 % \begin{macrocode}
-\newcommand{\rru}{\textbf{\textsf{u}}}
+\newcommand{\rru}{\@rr{u}}
 \newcommand{\Rubiku}{\@xyzRubik{u}}
 \newcommand{\rrhu}{\@xyzh{u}}
 %    \end{macrocode}
@@ -6691,9 +8126,9 @@
 %  \begin{macro}{\Rubikd}
 %  These commands  all draw forms which denote the d rotation.
 % \begin{macrocode}
-\newcommand{\rrd}{\textbf{\textsf{d}}}
-\newcommand{\Rubikd}{\@xyzRubik{d}}
-\newcommand{\rrhd}{\@xyzh{d}}
+\newcommand{\rrd}{\@rr{d}}
+\newcommand{\rrhd}{\@xyzhbdfl{d}}
+\newcommand{\Rubikd}{\@xyzbdflRubik{d}}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -6707,9 +8142,9 @@
 %  \begin{macro}{\Rubikl}
 %  These commands  all draw forms which denote the l rotation.
 % \begin{macrocode}
-\newcommand{\rrl}{\textbf{\textsf{l}}}
-\newcommand{\Rubikl}{\@xyzRubik{l}}
-\newcommand{\rrhl}{\@xyzh{l}}
+\newcommand{\rrl}{\@rr{l}}
+\newcommand{\rrhl}{\@xyzhbdfl{l}}
+\newcommand{\Rubikl}{\@xyzbdflRubik{l}}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -6719,7 +8154,7 @@
 %  \begin{macro}{\Rubikr}
 %  These commands  all draw forms which denote the r rotation.
 % \begin{macrocode}
-\newcommand{\rrr}{\textbf{\textsf{r}}}
+\newcommand{\rrr}{\@rr{r}}
 \newcommand{\Rubikr}{\@xyzRubik{r}}
 \newcommand{\rrhr}{\@xyzh{r}}
 %    \end{macrocode}
@@ -6735,9 +8170,9 @@
 %  \begin{macro}{\Rubikf}
 %  These commands  all draw forms which denote the f rotation.
 % \begin{macrocode}
-\newcommand{\rrf}{\textbf{\textsf{f}}}
-\newcommand{\Rubikf}{\@xyzRubik{f}}
-\newcommand{\rrhf}{\@xyzh{f}}
+\newcommand{\rrf}{\@rr{f}}
+\newcommand{\rrhf}{\@xyzhbdfl{f}}
+\newcommand{\Rubikf}{\@xyzbdflRubik{f}}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
@@ -6747,15 +8182,1703 @@
 %  \begin{macro}{\Rubikb}
 %  These commands  all draw forms which denote the b rotation.
 % \begin{macrocode}
-\newcommand{\rrb}{\textbf{\textsf{b}}}
-\newcommand{\Rubikb}{\@xyzRubik{b}}
-\newcommand{\rrhb}{\@xyzh{b}}
+\newcommand{\rrb}{\@rr{b}}
+\newcommand{\rrhb}{\@xyzhbdfl{b}}
+\newcommand{\Rubikb}{\@xyzbdflRubik{b}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%    \subsection{\hspace{3mm}Face(c) and Face(m) rotations}
+%      \label{sec:codeJaap}
+%
+% This subsection (added Nov 2016) is to accommodate some additional notation,
+% much used on the Jaap Puzzles website (Scherphius J), which, although quite 
+% convenient, is technically `non-standard'. This additional notation
+% makes available the (middle slice) rotations  of the form Rm, Rmp, Lm, Lmp, ... and 
+% also the  (whole cube) rotations Rc, Lc, ...   (referenced to a face) as  used on the 
+%  Cube Lovers usenet group (1981--1997). This notation was probably  invented by Singmaster
+% (see Scherphius J).
+%
+%  \begin{macro}{\@xyzhc}
+%  \begin{macro}{\@xyzhcp}
+%  \begin{macro}{\@xyzRubikc}
+%  \begin{macro}{\@xyzRubikcp}
+% First we have some useful facilitating commands we shall make use of in 
+% conjunction with the Face(c) and Face(cp) notation.
+% \begin{macrocode}
+\newcommand{\@xyzhc}[1]{[\raisebox{-1.2pt}%
+   {{\@rubikfont #1\@rubikfontFNS c}}]} 
+\newcommand{\@xyzhcp}[1]{[\raisebox{-1.2pt}%
+   {{\@rubikfont #1{\@rubikfontFNS c}\@rubikprime}}]}
+\newcommand{\@xyzRubikc}[1]{\raisebox{3.45pt}%
+   {[\raisebox{-1.2pt}{{\@rubikfont #1\@rubikfontFNS c}}]}}
+\newcommand{\@xyzRubikcp}[1]{\raisebox{3.45pt}%
+   {[\raisebox{-1.2pt}{{\@rubikfont #1{\@rubikfontFNS c}\@rubikprime}}]}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+% 
+%
+%  \subsubsection{\hspace{3mm}Rotations Rc and Rcp}
+%
+% Whole cube rotations  Rc = x, Rcp = xp.
+%
+%  \begin{macro}{\rrRc}
+%  \begin{macro}{\rrhRc}
+%  \begin{macro}{\RubikRc}
+%  These commands  all draw forms which denote the Rc rotation.
+% \begin{macrocode}
+\newcommand{\rrRc}{\@rrc{R}}
+\newcommand{\RubikRc}{\@xyzRubikc{R}}
+\newcommand{\rrhRc}{\@xyzhc{R}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrRcp}
+%  \begin{macro}{\rrhRcp}
+%  \begin{macro}{\RubikRcp}
+%  These commands  all draw forms which denote the Rcp rotation.
+% \begin{macrocode}
+\newcommand{\rrRcp}{\@rrcp{R}}
+\newcommand{\RubikRcp}{\@xyzRubikcp{R}}
+\newcommand{\rrhRcp}{\@xyzhcp{R}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%   \subsubsection{\hspace{3mm}Rotations Lc and Lcp}
+%
+% Whole cube rotations Lc = xp, Lcp = x.
+%
+%  \begin{macro}{\rrLc}
+%  \begin{macro}{\rrhLc}
+%  \begin{macro}{\RubikLc}
+%  These commands  all draw forms which denote the Lc rotation.
+% \begin{macrocode}
+\newcommand{\rrLc}{\@rrc{L}}
+\newcommand{\RubikLc}{\@xyzRubikc{L}}
+\newcommand{\rrhLc}{\@xyzhc{L}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrLcp}
+%  \begin{macro}{\rrhLcp}
+%  \begin{macro}{\RubikLcp}
+%  These commands  all draw forms which denote the Lcp rotation.
+% \begin{macrocode}
+\newcommand{\rrLcp}{\@rrcp{L}}
+\newcommand{\RubikLcp}{\@xyzRubikcp{L}}
+\newcommand{\rrhLcp}{\@xyzhcp{L}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%     \subsubsection{\hspace{3mm}Rotations Uc and Ucp}
+%
+% Whole cube rotation Uc = y, Ucp=yp.
+%
+%  \begin{macro}{\rrUc}
+%  \begin{macro}{\rrhUc}
+%  \begin{macro}{\RubikUc}
+%  These commands  all draw forms which denote the Uc rotation.
+% \begin{macrocode}
+\newcommand{\rrUc}{\@rrc{U}}
+\newcommand{\RubikUc}{\@xyzRubikc{U}}
+\newcommand{\rrhUc}{\@xyzhc{U}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrUcp}
+%  \begin{macro}{\rrhUcp}
+%  \begin{macro}{\RubikUcp}
+%  These commands  all draw forms which denote the Ucp rotation.
+% \begin{macrocode}
+\newcommand{\rrUcp}{\@rrcp{U}}
+\newcommand{\RubikUcp}{\@xyzRubikcp{U}}
+\newcommand{\rrhUcp}{\@xyzhcp{U}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+% 
+%  \subsubsection{\hspace{3mm}Rotations Dc and Dcp}
+%
+%  Whole cube rotations Dc = yp, Dcp = y.
+%
+%  \begin{macro}{\rrDc}
+%  \begin{macro}{\rrhDc}
+%  \begin{macro}{\RubikDc}
+%  These commands  all draw forms which denote the Dc rotation.
+% \begin{macrocode}
+\newcommand{\rrDc}{\@rrc{D}}
+\newcommand{\RubikDc}{\@xyzRubikc{D}}
+\newcommand{\rrhDc}{\@xyzhc{D}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrDcp}
+%  \begin{macro}{\rrhDcp}
+%  \begin{macro}{\RubikDcp}
+%  These commands  all draw forms which denote the Dcp rotation.
+% \begin{macrocode}
+\newcommand{\rrDcp}{\@rrcp{D}}
+\newcommand{\RubikDcp}{\@xyzRubikcp{D}}
+\newcommand{\rrhDcp}{\@xyzhcp{D}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%    \subsubsection{\hspace{3mm}Rotations Fc and Fcp}
+%
+%  Whole cube rotations Fc = z, Fcp = zp.
+%
+%  \begin{macro}{\rrFc}
+%  \begin{macro}{\rrhFc}
+%  \begin{macro}{\RubikFc}
+%  These commands  all draw forms which denote the Fc rotation.
+% \begin{macrocode}
+\newcommand{\rrFc}{\@rrc{F}}
+\newcommand{\RubikFc}{\@xyzRubikc{F}}
+\newcommand{\rrhFc}{\@xyzhc{F}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrFcp}
+%  \begin{macro}{\rrhFcp}
+%  \begin{macro}{\RubikFcp}
+%  These commands  all draw forms which denote the Fcp rotation.
+% \begin{macrocode}
+\newcommand{\rrFcp}{\@rrcp{F}}
+\newcommand{\RubikFcp}{\@xyzRubikcp{F}}
+\newcommand{\rrhFcp}{\@xyzhcp{F}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%   \subsubsection{\hspace{3mm}Rotations Bc and Bcp}
+%
+%   Whole cube rotation Bc = zp, Bcp = z.
+%
+%  \begin{macro}{\rrBc}
+%  \begin{macro}{\rrhBc}
+%  \begin{macro}{\RubikBc}
+%  These commands  all draw forms which denote the Bc rotation.
+% \begin{macrocode}
+\newcommand{\rrBc}{\@rrc{B}}
+\newcommand{\RubikBc}{\@xyzRubikc{B}}
+\newcommand{\rrhBc}{\@xyzhc{B}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrBcp}
+%  \begin{macro}{\rrhBcp}
+%  \begin{macro}{\RubikBcp}
+%  These commands  all draw forms which denote the Bcp rotation.
+% \begin{macrocode}
+\newcommand{\rrBcp}{\@rrcp{B}}
+\newcommand{\RubikBcp}{\@xyzRubikcp{B}}
+\newcommand{\rrhBcp}{\@xyzhcp{B}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%    \subsubsection{\hspace{3mm}Rotations Rm and Rmp}
+%
+% Rm = Mp= Sr  (M follows Left). We  use Sr and Srp as the templates.
+%
+%  \begin{macro}{\rrRm}
+%  \begin{macro}{\rrhRm}
+%  \begin{macro}{\RubikRm}
+%  \begin{macro}{\textRubikRm}
+%  These commands  draw forms of the Rm slice rotation.
+% \begin{macrocode}
+\newcommand{\rrRm}{\@rrm{R}}
+\newcommand{\rrhRm}{\rrhMp}%
+\newcommand{\RubikRm}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareMp\\
+\rrRm%
+\end{minipage}%
+}}
+\newcommand{\textRubikRm}{\rrRm\,\rrhMp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrRmp}
+%  \begin{macro}{\rrhRmp}
+%  \begin{macro}{\RubikRmp}
+%  \begin{macro}{\textRubikRmp}
+%  These commands  draw forms of the Rmp slice rotation.
+% \begin{macrocode}
+\newcommand{\rrRmp}{\@rrmp{R}}
+\newcommand{\rrhRmp}{\rrhM}%
+\newcommand{\RubikRmp}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareM\\
+\rrRmp%
+\end{minipage}%
+}}
+\newcommand{\textRubikRmp}{\rrRmp\,\rrhM}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations Lm and Lmp}
+%
+% Lm = M = Sl  (M follows Left). We  use Sl and Slp as the templates.
+%
+%  \begin{macro}{\rrLm}
+%  \begin{macro}{\rrhLm}
+%  \begin{macro}{\RubikLm}
+%  \begin{macro}{\textRubikLm}
+%  These commands  draw forms of the Lm slice rotation.
+% \begin{macrocode}
+\newcommand{\rrLm}{\@rrm{L}}
+\newcommand{\rrhLm}{\rrhM}%
+\newcommand{\RubikLm}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareM\\
+\rrLm%
+\end{minipage}%
+}}
+\newcommand{\textRubikLm}{\rrLm\,\rrhM}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrLmp}
+%  \begin{macro}{\rrhLmp}
+%  \begin{macro}{\RubikLmp}
+%  \begin{macro}{\textRubikLmp}
+%  These commands  draw forms of the Lmp slice rotation.
+% \begin{macrocode}
+\newcommand{\rrLmp}{\@rrmp{L}}
+\newcommand{\rrhLmp}{\rrhMp}%
+\newcommand{\RubikLmp}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareMp\\
+\rrLmp%
+\end{minipage}%
+}}
+\newcommand{\textRubikLmp}{\rrLmp\,\rrhMp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations Um and Ump}
+%
+%  Um = Ep = Su (E follows Down). We use  Su and Sup as the templates.
+%
+%  \begin{macro}{\rrUm}
+%  \begin{macro}{\rrhUm}
+%  \begin{macro}{\RubikUm}
+%  \begin{macro}{\textRubikUm}
+%  These commands  draw forms of the  Um slice rotation.
+%  We also need to fine-tune the spacing 
+%  between these `slice' hieroglyphs (especially Fs  and Bs).
+% \begin{macrocode}
+\newcommand{\rrUm}{\@rrm{U}}
+\newcommand{\rrhUm}{\rrhEp}%
+\newcommand{\RubikUm}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareEp\\
+\rrUm%
+\end{minipage}%
+}}
+\newcommand{\textRubikUm}{\rrUm\,\rrhEp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrUmp}
+%  \begin{macro}{\rrhUmp}
+%  \begin{macro}{\RubikUmp}
+%  \begin{macro}{\textRubikUmp}
+%  These commands  draw forms of the  Ump slice rotation.
+%  We also need to fine-tune the spacing 
+%  between these `slice' hieroglyphs (especially Fs  and Bs).
+% \begin{macrocode}
+\newcommand{\rrUmp}{\@rrmp{U}}
+\newcommand{\rrhUmp}{\rrhE}%
+\newcommand{\RubikUmp}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareE\\
+\rrUmp%
+\end{minipage}%
+}}
+\newcommand{\textRubikUmp}{\rrUmp\,\rrhE}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations Dm and Dmp}
+%
+%   Dm = E = Sd  (E follows Down). We use Sd and Sdp as the templates.
+%
+%  \begin{macro}{\rrDm}
+%  \begin{macro}{\rrhDm}
+%  \begin{macro}{\RubikDm}
+%  \begin{macro}{\textRubikDm}
+%  These commands  draw forms of the Singmaster Dm slice rotation.
+% \begin{macrocode}
+\newcommand{\rrDm}{\@rrm{D}}
+\newcommand{\rrhDm}{\rrhE}%
+\newcommand{\RubikDm}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareE\\
+\rrDm%
+\end{minipage}%
+}}
+\newcommand{\textRubikDm}{\rrDm\,\rrhE}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrDmp}
+%  \begin{macro}{\rrhDmp}
+%  \begin{macro}{\RubikDmp}
+%  \begin{macro}{\textRubikDmp}
+%  These commands  draw forms of the Singmaster Dmp slice rotation.
+% \begin{macrocode}
+\newcommand{\rrDmp}{\@rrmp{D}}
+\newcommand{\rrhDmp}{\rrhEp}%
+\newcommand{\RubikDmp}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareEp\\
+\rrDmp%
+\end{minipage}%
+}}
+\newcommand{\textRubikDmp}{\rrDmp\,\rrhEp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations Fm and Fmp}
+% 
+% Fm = S =  Sf  (S follows Front).
+% S is not visible from the front, so is represented in a square box.
+% We use Sf and Sfp as the templates.
+%
+%  \begin{macro}{\rrFm}
+%  \begin{macro}{\rrhFm}
+%  \begin{macro}{\RubikFm}
+%  \begin{macro}{\textRubikFm}
+%  These commands  draw forms of the  Fm slice rotation.
+%  We need to just make square with Fm in square; 
+%  adjust box height using a \cmd{\rule};
+%  adjust \cmd{\fboxsep} (default=3pt);
+%  adjust \cmd{\fboxrule} (default=0.4pt);
+%  bounded by \{\} so no need to reset to defaults.
+% Not visible from the front.
+% \begin{macrocode}
+\newcommand{\rrFm}{\@rrm{F}}
+\newcommand{\SquareFm}{\@tlen\@SquareLetter{\rrFm}\@tlen}
+\newcommand{\rrhFm}{\raisebox{-0.25mm}{\SquareFm}}
+\newcommand{\RubikFm}{\raisebox{\@hRubik}{\SquareFm}}
+\newcommand{\textRubikFm}{\rrhFm}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrFmp}
+%  \begin{macro}{\rrhFmp}
+%  \begin{macro}{\RubikFmp}
+%  \begin{macro}{\textRubikFmp}
+%  These commands  draw forms of the  Fmp slice rotation.
+%  We need to just make square with Fmp in square; 
+%  adjust box height using a \cmd{\rule};
+%  adjust \cmd{\fboxsep} (default=3pt);
+%  adjust \cmd{\fboxrule} (default=0.4pt);
+%  bounded by \{\} so no need to reset to defaults.
+% Not visible from the front.
+% \begin{macrocode}
+\newcommand{\rrFmp}{\@rrmp{F}}
+\newcommand{\SquareFmp}{\@tlen\@SquareLetter{\rrFmp}\@tlen}
+\newcommand{\rrhFmp}{\raisebox{-0.25mm}{\SquareFmp}}
+\newcommand{\RubikFmp}{\raisebox{\@hRubik}{\SquareFmp}}
+\newcommand{\textRubikFmp}{\rrhFmp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations Bm and Bmp}
+%
+%   Bm = Sp =  Sb. We use Sb and Sbp as the templates.   
+%
+%  \begin{macro}{\rrBm}
+%  \begin{macro}{\rrhBm}
+%  \begin{macro}{\RubikBm}
+%  \begin{macro}{\textRubikBm}
+%  These commands  draw forms of the  Bm slice rotation.
+%  We need to just make square with Bm in square; 
+%  adjust box height using a \cmd{\rule};
+%  adjust \cmd{\fboxsep} (default=3pt);
+%  adjust \cmd{\fboxrule} (default=0.4pt);
+%  bounded by \{\} so no need to reset to defaults.
+% Not visible from the front.
+% \begin{macrocode}
+\newcommand{\rrBm}{\@rrm{B}}
+\newcommand{\SquareBm}{\@tlen\@SquareLetter{\rrBm}\@tlen}
+\newcommand{\rrhBm}{\raisebox{-0.25mm}{\SquareBm}}
+\newcommand{\RubikBm}{\raisebox{\@hRubik}{\SquareBm}}
+\newcommand{\textRubikBm}{\rrhBm}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrBmp}
+%  \begin{macro}{\rrhBmp}
+%  \begin{macro}{\RubikBmp}
+%  \begin{macro}{\textRubikBmp}
+%  These commands  draw forms of the Bmp slice rotation.
+%  We need to just make square with Bmp in square; 
+%  adjust box height using a \cmd{\rule};
+%  adjust \cmd{\fboxsep} (default=3pt);
+%  adjust \cmd{\fboxrule} (default=0.4pt);
+%  bounded by \{\} so no need to reset to defaults.
+% Not visible from the front.
+% \begin{macrocode}
+\newcommand{\rrBmp}{\@rrmp{B}}
+\newcommand{\SquareBmp}{\@tlen\@SquareLetter{\rrBmp}\@tlen}
+\newcommand{\rrhBmp}{\raisebox{-0.25mm}{\SquareBmp}}
+\newcommand{\RubikBmp}{\raisebox{\@hRubik}{\SquareBmp}}
+\newcommand{\textRubikBmp}{\rrhBmp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%
+%
+%    \subsection{\hspace{3mm}Randelshofer superset ENG rotations (CMST)}
+%      \label{sec:codeRandelshofer}
+%
+% (see webpage: \verb!Randelshofer.ch/rubik/patterns/doc/supersetENG_3x3.html!)
+% 
+% This section relates to the recent Rubik  notation developed 
+% by Randelshofer (see URL above),  known as the ``superset ENG rotations''
+% (see Sections~\ref{sec:RubikCommands} and \ref{sec:listofRandelshofercommands}
+% for details).
+%
+% I denote this  notation as ``CMST'' (i.e.,~his C, M, S and T notation).
+% Although this notation replicates previously existing World Cube Association notation, 
+% we include it here for completeness. Fortunately the Randelshofer notation does 
+% not conflict with existing notation.
+%
+% Briefly, the CMST letters  denote whole Cube, Middle, outer-Slice and wide (T)
+% rotations associated with named faces. For example, the rotation-code  MR
+% indicates a rotation of the  middle slice parallel to the \textsc{right} face, 
+% and in the same  sense (direction) as \rr{R}\ (see Section~\ref{sec:RubikCommands}  for details).
+%
+% 
+% First we make some useful facilitating commands for the CX1 and CX1p forms
+% as these are handled with raised  square brackets.
+% We model these four macros on the equivalent 
+% \verb!\@xyzh!, \verb!\@xyzhp!,\verb!\@xyzRubik!,\verb!\@xyzRubikp! macros defined above.
+% \begin{macrocode}
+\newcommand{\@randhc}[1]{[\raisebox{-1.2pt}{{\@rubikfont C#1}}]}
+\newcommand{\@randhcp}[1]{[\raisebox{-1.2pt}{{\@rubikfont C#1\@rubikprime}}]}
+\newcommand{\@randRubikc}[1]%
+   {\raisebox{3.45pt}{[\raisebox{-1.2pt}{{\@rubikfont C#1}}]}}
+\newcommand{\@randRubikcp}[1]%
+   {\raisebox{3.45pt}{[\raisebox{-1.2pt}{{\@rubikfont C#1\@rubikprime}}]}}
+%    \end{macrocode}
+%
+%
+% In the following we create the base form of a rotation code, eg \rrhCR\ and then
+% the user typesets this rotation using CR as the argument for \verb!\rrh{}!. 
+% This works because the macro \verb!\@join{}{}! is used to join \cmd{\rrh} 
+% and CR $\rightarrow$ \cmd{\rrhCR} etc.
+%
+% The = signs at the beginning of each new section indicate the equivalence
+% between the Randelshofer notation and the current (World Cube Association)
+% notation. 
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations CR and CRp}
+%
+% Whole cube rotations CR = Rc = x, CRp = Rcp = xp.
+%
+%  \begin{macro}{\rrCR}
+%  \begin{macro}{\rrhCR}
+%  \begin{macro}{\RubikCR}
+%  These commands  all draw forms which denote the CR = Rc rotation.
+% \begin{macrocode}
+\newcommand{\rrCR}{\@rr{CR}}
+\newcommand{\RubikCR}{\@randRubikc{R}}
+\newcommand{\rrhCR}{\@randhc{R}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrCRp}
+%  \begin{macro}{\rrhCRp}
+%  \begin{macro}{\RubikCRp}
+%  These commands  all draw forms which denote the CRp =  Rcp rotation.
+% \begin{macrocode}
+\newcommand{\rrCRp}{\@rrp{CR}}
+\newcommand{\RubikCRp}{\@randRubikcp{R}}
+\newcommand{\rrhCRp}{\@randhcp{R}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%   \subsubsection{\hspace{3mm}Rotations CL and CLp}
+%
+% Whole cube rotations  CL = Lc = xp, CLp = Lcp = x.
+%
+%  \begin{macro}{\rrCL}
+%  \begin{macro}{\rrhCL}
+%  \begin{macro}{\RubikCL}
+%  These commands  all draw forms which denote the CL rotation.
+% \begin{macrocode}
+\newcommand{\rrCL}{\@rr{CL}}
+\newcommand{\RubikCL}{\@randRubikc{L}}
+\newcommand{\rrhCL}{\@randhc{L}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrCLp}
+%  \begin{macro}{\rrhCLp}
+%  \begin{macro}{\RubikCLp}
+%  These commands  all draw forms which denote the CLp rotation.
+% \begin{macrocode}
+\newcommand{\rrCLp}{\@rrp{CL}}
+\newcommand{\RubikCLp}{\@randRubikcp{L}}
+\newcommand{\rrhCLp}{\@randhcp{L}}
 %    \end{macrocode}
 %    \end{macro}
 %    \end{macro}
 %    \end{macro}
 %
 %
+%     \subsubsection{\hspace{3mm}Rotations CU and CUp}
+%
+% Whole cube rotation CU = Uc = y, CUp = Ucp=yp.
+%
+%  \begin{macro}{\rrCU}
+%  \begin{macro}{\rrhCU}
+%  \begin{macro}{\RubikCU}
+%  These commands  all draw forms which denote the CU rotation.
+% \begin{macrocode}
+\newcommand{\rrCU}{\@rr{CU}}
+\newcommand{\RubikCU}{\@randRubikc{U}}
+\newcommand{\rrhCU}{\@randhc{U}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrCUp}
+%  \begin{macro}{\rrhCUp}
+%  \begin{macro}{\RubikCUp}
+%  These commands  all draw forms which denote the CUp rotation.
+% \begin{macrocode}
+\newcommand{\rrCUp}{\@rrp{CU}}
+\newcommand{\RubikCUp}{\@randRubikcp{U}}
+\newcommand{\rrhCUp}{\@randhcp{U}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+% 
+%  \subsubsection{\hspace{3mm}Rotations CD and CDp}
+%
+%  Whole cube rotations CD = Dc = yp, CDp = Dcp = y.
+%
+%  \begin{macro}{\rrCD}
+%  \begin{macro}{\rrhCD}
+%  \begin{macro}{\RubikCD}
+%  These commands  all draw forms which denote the CD rotation.
+% \begin{macrocode}
+\newcommand{\rrCD}{\@rr{CD}}
+\newcommand{\RubikCD}{\@randRubikc{D}}
+\newcommand{\rrhCD}{\@randhc{D}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrCDp}
+%  \begin{macro}{\rrhCDp}
+%  \begin{macro}{\RubikCDp}
+%  These commands  all draw forms which denote the CDp rotation.
+% \begin{macrocode}
+\newcommand{\rrCDp}{\@rrp{CD}}
+\newcommand{\RubikCDp}{\@randRubikcp{D}}
+\newcommand{\rrhCDp}{\@randhcp{D}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%    \subsubsection{\hspace{3mm}Rotations CF and CFp}
+%
+%  Whole cube rotations CF = Fc = z, CFp = Fcp = zp.
+%
+%  \begin{macro}{\rrCF}
+%  \begin{macro}{\rrhCF}
+%  \begin{macro}{\RubikCF}
+%  These commands  all draw forms which denote the CF rotation.
+% \begin{macrocode}
+\newcommand{\rrCF}{\@rr{CF}}
+\newcommand{\RubikCF}{\@randRubikc{F}}
+\newcommand{\rrhCF}{\@randhc{F}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrCFp}
+%  \begin{macro}{\rrhCFp}
+%  \begin{macro}{\RubikCFp}
+%  These commands  all draw forms which denote the CFp rotation.
+% \begin{macrocode}
+\newcommand{\rrCFp}{\@rrp{CF}}
+\newcommand{\RubikCFp}{\@randRubikcp{F}}
+\newcommand{\rrhCFp}{\@randhcp{F}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%   \subsubsection{\hspace{3mm}Rotations CB and CBp}
+%
+%   Whole cube rotation CB = Bc = zp, CBp = Bcp = z.
+%
+%  \begin{macro}{\rrCB}
+%  \begin{macro}{\rrhCB}
+%  \begin{macro}{\RubikCB}
+%  These commands  all draw forms which denote the CB rotation.
+% \begin{macrocode}
+\newcommand{\rrCB}{\@rr{CB}}
+\newcommand{\RubikCB}{\@randRubikc{B}}
+\newcommand{\rrhCB}{\@randhc{B}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrCBp}
+%  \begin{macro}{\rrhCBp}
+%  \begin{macro}{\RubikCBp}
+%  These commands  all draw forms which denote the CBp rotation.
+% \begin{macrocode}
+\newcommand{\rrCBp}{\@rrp{CB}}
+\newcommand{\RubikCBp}{\@randRubikcp{B}}
+\newcommand{\rrhCBp}{\@randhcp{B}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%
+%    \subsubsection{\hspace{3mm}Rotations MR and MRp}
+%
+% MR = Rm = Mp= Sr  (M follows Left). We  use Sr and Srp as the templates.
+%
+%  \begin{macro}{\rrMR}
+%  \begin{macro}{\rrhMR}
+%  \begin{macro}{\RubikMR}
+%  \begin{macro}{\textRubikMR}
+%  These commands  draw forms of the MR middle slice rotation.
+% \begin{macrocode}
+\newcommand{\rrMR}{\@rr{MR}}
+\newcommand{\rrhMR}{\rrhMp}%
+\newcommand{\RubikMR}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareMp\\
+\rrMR%
+\end{minipage}%
+}}
+\newcommand{\textRubikMR}{\rrMR\,\rrhMp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrMRp}
+%  \begin{macro}{\rrhMRp}
+%  \begin{macro}{\RubikMRp}
+%  \begin{macro}{\textRubikMRp}
+%  These commands  draw forms of the MRp slice rotation.
+% \begin{macrocode}
+\newcommand{\rrMRp}{\@rrp{MR}}
+\newcommand{\rrhMRp}{\rrhM}%
+\newcommand{\RubikMRp}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareM\\
+\rrMRp%
+\end{minipage}%
+}}
+\newcommand{\textRubikMRp}{\rrMRp\,\rrhM}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations ML and MLp}
+%
+% ML =  Lm = M = Sl  (M follows Left). We  use Sl and Slp as the templates.
+%
+%  \begin{macro}{\rrML}
+%  \begin{macro}{\rrhML}
+%  \begin{macro}{\RubikML}
+%  \begin{macro}{\textRubikML}
+%  These commands  draw forms of the ML slice rotation.
+% \begin{macrocode}
+\newcommand{\rrML}{\@rr{ML}}
+\newcommand{\rrhML}{\rrhM}%
+\newcommand{\RubikML}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareM\\
+\rrML%
+\end{minipage}%
+}}
+\newcommand{\textRubikML}{\rrML\,\rrhM}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrMLp}
+%  \begin{macro}{\rrhMLp}
+%  \begin{macro}{\RubikMLp}
+%  \begin{macro}{\textRubikMLp}
+%  These commands  draw forms of the MLp slice rotation.
+% \begin{macrocode}
+\newcommand{\rrMLp}{\@rrp{ML}}
+\newcommand{\rrhMLp}{\rrhMp}%
+\newcommand{\RubikMLp}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareMp\\
+\rrMLp%
+\end{minipage}%
+}}
+\newcommand{\textRubikMLp}{\rrMLp\,\rrhMp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations MU and MUp}
+%
+%  MU =  Um = Ep = Su (E follows Down). We use  Su and Sup as the templates.
+%
+%  \begin{macro}{\rrMU}
+%  \begin{macro}{\rrhMU}
+%  \begin{macro}{\RubikMU}
+%  \begin{macro}{\textRubikMU}
+%  These commands  draw forms of the  MU slice rotation.
+% \begin{macrocode}
+\newcommand{\rrMU}{\@rr{MU}}
+\newcommand{\rrhMU}{\rrhEp}%
+\newcommand{\RubikMU}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareEp\\
+\rrMU%
+\end{minipage}%
+}}
+\newcommand{\textRubikMU}{\rrMU\,\rrhEp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrMUp}
+%  \begin{macro}{\rrhMUp}
+%  \begin{macro}{\RubikMUp}
+%  \begin{macro}{\textRubikMUp}
+%  These commands  draw forms of the  MUp slice rotation.
+% \begin{macrocode}
+\newcommand{\rrMUp}{\@rrp{MU}}
+\newcommand{\rrhMUp}{\rrhE}%
+\newcommand{\RubikMUp}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareE\\
+\rrMUp%
+\end{minipage}%
+}}
+\newcommand{\textRubikMUp}{\rrMUp\,\rrhE}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations MD and MDp}
+%
+% MD =  Dm = E = Sd  (E follows Down). We use Sd and Sdp as the templates.
+%
+%  \begin{macro}{\rrMD}
+%  \begin{macro}{\rrhMD}
+%  \begin{macro}{\RubikMD}
+%  \begin{macro}{\textRubikMD}
+%  These commands  draw forms of the Randelshofer MD slice rotation.
+% \begin{macrocode}
+\newcommand{\rrMD}{\@rr{MD}}
+\newcommand{\rrhMD}{\rrhE}%
+\newcommand{\RubikMD}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareE\\
+\rrMD%
+\end{minipage}%
+}}
+\newcommand{\textRubikMD}{\rrMD\,\rrhE}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrMDp}
+%  \begin{macro}{\rrhMDp}
+%  \begin{macro}{\RubikMDp}
+%  \begin{macro}{\textRubikMDp}
+%  These commands  draw forms of the Randelshofer MDp slice rotation.
+% \begin{macrocode}
+\newcommand{\rrMDp}{\@rrp{MD}}
+\newcommand{\rrhMDp}{\rrhEp}%
+\newcommand{\RubikMDp}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareEp\\
+\rrMDp%
+\end{minipage}%
+}}
+\newcommand{\textRubikMDp}{\rrMDp\,\rrhEp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations MF and MFp}
+% 
+% MF = Fm = S = Sf  (S follows Front).
+% MF = S is not visible from the front, so is represented in a square box.
+% We use Sf and Sfp as the templates.
+%
+%  \begin{macro}{\rrMF}
+%  \begin{macro}{\rrhMF}
+%  \begin{macro}{\RubikMF}
+%  \begin{macro}{\textRubikMF}
+%  These commands  draw forms of the  MF slice rotation.
+%  We need to just make square with MF in square; 
+%  adjust box height using a \cmd{\rule};
+%  adjust \cmd{\fboxsep} (default=3pt);
+%  adjust \cmd{\fboxrule} (default=0.4pt);
+%  bounded by \{\} so no need to reset to defaults.
+% Not visible from the front.
+% \begin{macrocode}
+\newcommand{\rrMF}{\@rr{MF}}
+\newcommand{\SquareMF}{\@tlen\@SquareLetter{\rrMF}\@tlen}
+\newcommand{\rrhMF}{\raisebox{-0.25mm}{\SquareMF}}
+\newcommand{\RubikMF}{\raisebox{\@hRubik}{\SquareMF}}
+\newcommand{\textRubikMF}{\rrhMF}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrMFp}
+%  \begin{macro}{\rrhMFp}
+%  \begin{macro}{\RubikMFp}
+%  \begin{macro}{\textRubikMFp}
+%  These commands  draw forms of the  MFp slice rotation.
+%  We need to just make square with MFp in square; 
+%  adjust box height using a \cmd{\rule};
+%  adjust \cmd{\fboxsep} (default=3pt);
+%  adjust \cmd{\fboxrule} (default=0.4pt);
+%  bounded by \{\} so no need to reset to defaults.
+% Not visible from the front.
+% \begin{macrocode}
+\newcommand{\rrMFp}{\@rrp{MF}}
+\newcommand{\SquareMFp}{\@tlen\@SquareLetter{\rrMFp}\@tlen}
+\newcommand{\rrhMFp}{\raisebox{-0.25mm}{\SquareMFp}}
+\newcommand{\RubikMFp}{\raisebox{\@hRubik}{\SquareMFp}}
+\newcommand{\textRubikMFp}{\rrhMFp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations MB and MBp}
+%
+%  MB = Bm = Sp =  Sb. We use Sb and Sbp as the templates.   
+%
+%  \begin{macro}{\rrMB}
+%  \begin{macro}{\rrhMB}
+%  \begin{macro}{\RubikMB}
+%  \begin{macro}{\textRubikMB}
+%  These commands  draw forms of the  MB slice rotation.
+%  We need to just make square with MB in square; 
+%  adjust box height using a \cmd{\rule};
+%  adjust \cmd{\fboxsep} (default=3pt);
+%  adjust \cmd{\fboxrule} (default=0.4pt);
+%  bounded by \{\} so no need to reset to defaults.
+% Not visible from the front.
+% \begin{macrocode}
+\newcommand{\rrMB}{\@rr{MB}}
+\newcommand{\SquareMB}{\@tlen\@SquareLetter{\rrMB}\@tlen}
+\newcommand{\rrhMB}{\raisebox{-0.25mm}{\SquareMB}}
+\newcommand{\RubikMB}{\raisebox{\@hRubik}{\SquareMB}}
+\newcommand{\textRubikMB}{\rrhMB}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrMBp}
+%  \begin{macro}{\rrhMBp}
+%  \begin{macro}{\RubikMBp}
+%  \begin{macro}{\textRubikMBp}
+%  These commands  draw forms of the MBp slice rotation.
+%  We need to just make square with MBp in square; 
+%  adjust box height using a \cmd{\rule};
+%  adjust \cmd{\fboxsep} (default=3pt);
+%  adjust \cmd{\fboxrule} (default=0.4pt);
+%  bounded by \{\} so no need to reset to defaults.
+% Not visible from the front.
+% \begin{macrocode}
+\newcommand{\rrMBp}{\@rrp{MB}}
+\newcommand{\SquareMBp}{\@tlen\@SquareLetter{\rrMBp}\@tlen}
+\newcommand{\rrhMBp}{\raisebox{-0.25mm}{\SquareMBp}}
+\newcommand{\RubikMBp}{\raisebox{\@hRubik}{\SquareMBp}}
+\newcommand{\textRubikMBp}{\rrhMBp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations T (wide)}
+% 
+% TR = Rw \ \ (We use Rw and Rwp as the templates).
+%
+% {\noindent}We first set up some useful T and Tp macros for use with (L,R,U,D,F,B)
+% slightly more general than before. As before the  rubikfont command needs to be 
+% delimited using two curly brackets to contain the font expression.
+% \begin{macrocode}
+\newcommand{\@rrT}[1]{{\@rubikfont T#1}}
+\newcommand{\@rrhT}[1]{\@join{\rrh#1}{w}}%
+\newcommand{\@textRubikT}[1]{\@rrT{#1}\,\@join{\rrh#1}{w}}
+%
+\newcommand{\@RubikT}[1]{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%%
+\@join{\Square#1}{w}\\%
+\@rrT{#1}%%
+\end{minipage}%
+}}
+%%
+\newcommand{\@rrTp}[1]{{\@rubikfont T#1\@rubikprime}}
+\newcommand{\@rrhTp}[1]{\@join{\rrh#1}{wp}}%
+\newcommand{\@textRubikTp}[1]{\@rrTp{#1}\,\@join{\rrh#1}{wp}}
+%%
+\newcommand{\@RubikTp}[1]{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%%
+\@join{\Square#1}{wp}\\%
+\@rrTp{#1}%%
+\end{minipage}%
+}}
+%    \end{macrocode}
+%
+%
+%
+%  \begin{macro}{\rrTL}
+%  \begin{macro}{\rrhTL}
+%  \begin{macro}{\RubikTL}
+%  \begin{macro}{\textRubikTL}
+%  These commands  draw forms of the TL = Lw wide slice rotation.
+% \begin{macrocode}
+\newcommand{\rrTL}{\@rrT{L}}% = rrLw
+\newcommand{\rrhTL}{\@rrhT{L}}
+\newcommand{\textRubikTL}{\@textRubikT{L}}
+\newcommand{\RubikTL}{\@RubikT{L}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%  \begin{macro}{\rrTLp}
+%  \begin{macro}{\rrhTLp}
+%  \begin{macro}{\RubikTLp}
+%  \begin{macro}{\textRubikTLp}
+%  These commands  draw forms of the TLp = Lwp wide slice rotation.
+% \begin{macrocode}
+\newcommand{\rrTLp}{\@rrTp{L}}
+\newcommand{\rrhTLp}{\@rrhTp{L}}
+\newcommand{\textRubikTLp}{\@textRubikTp{L}}
+\newcommand{\RubikTLp}{\@RubikTp{L}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%
+%  \begin{macro}{\rrTR}
+%  \begin{macro}{\rrhTR}
+%  \begin{macro}{\RubikTR}
+%  \begin{macro}{\textRubikTR}
+%  These commands  draw forms of the TR = Rw wide slice rotation.
+% \begin{macrocode}
+\newcommand{\rrTR}{\@rrT{R}}
+\newcommand{\rrhTR}{\@rrhT{R}}
+\newcommand{\textRubikTR}{\@textRubikT{R}}
+\newcommand{\RubikTR}{\@RubikT{R}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%  \begin{macro}{\rrTRp}
+%  \begin{macro}{\rrhTRp}
+%  \begin{macro}{\RubikTRp}
+%  \begin{macro}{\textRubikTRp}
+%  These commands  draw forms of the TRp = Rmp wide slice rotation.
+% \begin{macrocode}
+\newcommand{\rrTRp}{\@rrTp{R}}
+\newcommand{\rrhTRp}{\@rrhTp{R}}
+\newcommand{\textRubikTRp}{\@textRubikTp{R}}
+\newcommand{\RubikTRp}{\@RubikTp{R}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%
+%  \begin{macro}{\rrTU}
+%  \begin{macro}{\rrhTU}
+%  \begin{macro}{\RubikTU}
+%  \begin{macro}{\textRubikTU}
+%  These commands  draw forms of the TU = Uw wide slice rotation.
+% \begin{macrocode}
+\newcommand{\rrTU}{\@rrT{U}}
+\newcommand{\rrhTU}{\@rrhT{U}}
+\newcommand{\textRubikTU}{\@textRubikT{U}}
+\newcommand{\RubikTU}{\@RubikT{U}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%  \begin{macro}{\rrTUp}
+%  \begin{macro}{\rrhTUp}
+%  \begin{macro}{\RubikTUp}
+%  \begin{macro}{\textRubikTUp}
+%  These commands  draw forms of the TUp = Uwp wide slice rotation.
+% \begin{macrocode}
+\newcommand{\rrTUp}{\@rrTp{U}}
+\newcommand{\rrhTUp}{\@rrhTp{U}}
+\newcommand{\textRubikTUp}{\@textRubikTp{U}}
+\newcommand{\RubikTUp}{\@RubikTp{U}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+% 
+%
+%  \begin{macro}{\rrTD}
+%  \begin{macro}{\rrhTD}
+%  \begin{macro}{\RubikTD}
+%  \begin{macro}{\textRubikTD}
+%  These commands  draw forms of the TD = Dw wide slice rotation.
+% \begin{macrocode}
+\newcommand{\rrTD}{\@rrT{D}}
+\newcommand{\rrhTD}{\@rrhT{D}}
+\newcommand{\textRubikTD}{\@textRubikT{D}}
+\newcommand{\RubikTD}{\@RubikT{D}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%  \begin{macro}{\rrTDp}
+%  \begin{macro}{\rrhTDp}
+%  \begin{macro}{\RubikTDp}
+%  \begin{macro}{\textRubikTDp}
+%  These commands  draw forms of the TDp = Dwp wide slice rotation.
+% \begin{macrocode}
+\newcommand{\rrTDp}{\@rrTp{D}}
+\newcommand{\rrhTDp}{\@rrhTp{D}}
+\newcommand{\textRubikTDp}{\@textRubikTp{D}}
+\newcommand{\RubikTDp}{\@RubikTp{D}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+% 
+%  \begin{macro}{\rrTF}
+%  \begin{macro}{\rrhTF}
+%  \begin{macro}{\RubikTF}
+%  \begin{macro}{\textRubikTF}
+%  These commands  draw forms of the TF = Fw wide slice rotation.
+% \begin{macrocode}
+\newcommand{\rrTF}{\@rrT{F}}
+\newcommand{\rrhTF}{\@rrhT{F}}
+\newcommand{\textRubikTF}{\@textRubikT{F}}
+\newcommand{\RubikTF}{\@RubikT{F}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%  \begin{macro}{\rrTFp}
+%  \begin{macro}{\rrhTFp}
+%  \begin{macro}{\RubikTFp}
+%  \begin{macro}{\textRubikTFp}
+%  These commands  draw forms of the TFp = Fwp wide slice rotation.
+% \begin{macrocode}
+\newcommand{\rrTFp}{\@rrTp{F}}
+\newcommand{\rrhTFp}{\@rrhTp{F}}
+\newcommand{\textRubikTFp}{\@textRubikTp{F}}
+\newcommand{\RubikTFp}{\@RubikTp{F}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+% 
+%
+%  \begin{macro}{\rrTB}
+%  \begin{macro}{\rrhTB}
+%  \begin{macro}{\RubikTB}
+%  \begin{macro}{\textRubikTB}
+%  These commands  draw forms of the TB = Bw wide slice rotation.
+%  NOTE we just use the letters TB in a square
+% \begin{macrocode}
+\newcommand{\rrTB}{\@rrT{B}}
+\newcommand{\SquareTB}{\@tlen\@SquareLetter{\rrTB}\@tlen}
+\newcommand{\rrhTB}{\raisebox{-0.25mm}{\SquareTB}}
+\newcommand{\textRubikTB}{\rrhTB}
+\newcommand{\RubikTB}{\raisebox{\@hRubik}{\SquareTB}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%  \begin{macro}{\rrTBp}
+%  \begin{macro}{\rrhTBp}
+%  \begin{macro}{\RubikTBp}
+%  \begin{macro}{\textRubikTBp}
+%  These commands  draw forms of the TBp = Bwp wide slice rotation.
+%  NOTE we just use the letters TB' in a square
+% \begin{macrocode}
+\newcommand{\rrTBp}{\@rrTp{B}}
+\newcommand{\SquareTBp}{\@tlen\@SquareLetter{\rrTBp}\@tlen}
+\newcommand{\rrhTBp}{\raisebox{-0.25mm}{\SquareTBp}}
+\newcommand{\textRubikTBp}{\rrhTBp}
+\newcommand{\RubikTBp}{\raisebox{\@hRubik}{\SquareTBp}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations SR and SRp  (opposite slices)}
+%
+%  opposite slices in same direction
+% SR = Rs (both rotating in R direction)
+%
+%  \begin{macro}{\rrSR}
+%  \begin{macro}{\rrhSR}
+%  \begin{macro}{\RubikSR}
+%  \begin{macro}{\textRubikSR}
+%  These commands  draw forms of the SR opposite slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSR}{\@rr{SR}}
+\newcommand{\rrhSR}{\rrhRs}% 
+\newcommand{\RubikSR}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareRs\\
+\rrSR%
+\end{minipage}%
+}}
+\newcommand{\textRubikSR}{\rrSR\,\rrhRs}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrSRp}
+%  \begin{macro}{\rrhSRp}
+%  \begin{macro}{\RubikSRp}
+%  \begin{macro}{\textRubikSRp}
+%  These commands  draw forms of the SRp opposite slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSRp}{\@rrp{SR}}
+\newcommand{\rrhSRp}{\rrhRsp}%
+\newcommand{\RubikSRp}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareRsp\\
+\rrSRp%
+\end{minipage}%
+}}
+\newcommand{\textRubikSRp}{\rrSRp\,\rrhRsp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations SL and SLp}
+%
+% SL = Ls (both rotating in L direction)
+%
+%  \begin{macro}{\rrSL}
+%  \begin{macro}{\rrhSL}
+%  \begin{macro}{\RubikSL}
+%  \begin{macro}{\textRubikSL}
+%  These commands  draw forms of the SL opposite slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSL}{\@rr{SL}}
+\newcommand{\rrhSL}{\rrhLs}% 
+\newcommand{\RubikSL}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareLs\\
+\rrSL%
+\end{minipage}%
+}}
+\newcommand{\textRubikSL}{\rrSL\,\rrhLs}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrSLp}
+%  \begin{macro}{\rrhSLp}
+%  \begin{macro}{\RubikSLp}
+%  \begin{macro}{\textRubikSLp}
+%  These commands  draw forms of the SLp opposite slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSLp}{\@rrp{SL}}
+\newcommand{\rrhSLp}{\rrhLsp}%
+\newcommand{\RubikSLp}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareLsp\\
+\rrSLp%
+\end{minipage}%
+}}
+\newcommand{\textRubikSLp}{\rrSLp\,\rrhLsp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations SU and SUp}
+%
+% SU = Us (both rotating in U direction)
+%
+%  \begin{macro}{\rrSU}
+%  \begin{macro}{\rrhSU}
+%  \begin{macro}{\RubikSU}
+%  \begin{macro}{\textRubikSU}
+%  These commands  draw forms of the SU opposite slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSU}{\@rr{SU}}
+\newcommand{\rrhSU}{\rrhUs}% 
+\newcommand{\RubikSU}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareUs\\
+\rrSU%
+\end{minipage}%
+}}
+\newcommand{\textRubikSU}{\rrSU\,\rrhUs}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrSUp}
+%  \begin{macro}{\rrhSUp}
+%  \begin{macro}{\RubikSUp}
+%  \begin{macro}{\textRubikSUp}
+%  These commands  draw forms of the SUp opposite slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSUp}{\@rrp{SU}}
+\newcommand{\rrhSUp}{\rrhUsp}%
+\newcommand{\RubikSUp}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareUsp\\
+\rrSUp%
+\end{minipage}%
+}}
+\newcommand{\textRubikSUp}{\rrSUp\,\rrhUsp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations SD and SDp}
+%
+% SD = Ds (both rotating in D direction)
+%
+%  \begin{macro}{\rrSD}
+%  \begin{macro}{\rrhSD}
+%  \begin{macro}{\RubikSD}
+%  \begin{macro}{\textRubikSD}
+%  These commands  draw forms of the SD opposite slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSD}{\@rr{SD}}
+\newcommand{\rrhSD}{\rrhDs}% 
+\newcommand{\RubikSD}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareDs\\
+\rrSD%
+\end{minipage}%
+}}
+\newcommand{\textRubikSD}{\rrSD\,\rrhDs}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrSDp}
+%  \begin{macro}{\rrhSDp}
+%  \begin{macro}{\RubikSDp}
+%  \begin{macro}{\textRubikSDp}
+%  These commands  draw forms of the SDp opposite slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSDp}{\@rrp{SD}}
+\newcommand{\rrhSDp}{\rrhDsp}%
+\newcommand{\RubikSDp}{%
+{\@rubikfont%
+\begin{minipage}{0.6cm}
+\centering%
+\SquareDsp\\
+\rrSDp%
+\end{minipage}%
+}}
+\newcommand{\textRubikSDp}{\rrSDp\,\rrhDsp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{\hspace{3mm}Rotations SF and SFp}
+% 
+% SF = Fs is not visible from the front, so is represented in a square box.
+% Both rotating in the F direction
+% We use Fs and Fsp as the templates.
+%
+%  \begin{macro}{\rrSF}
+%  \begin{macro}{\rrhSF}
+%  \begin{macro}{\RubikSF}
+%  \begin{macro}{\textRubikSF}
+%  These commands  draw forms of the  SF opposite slice rotation.
+%  We need to just make square with SF in square; 
+%  adjust box height using a \cmd{\rule};
+%  adjust \cmd{\fboxsep} (default=3pt);
+%  adjust \cmd{\fboxrule} (default=0.4pt);
+%  bounded by \{\} so no need to reset to defaults.
+% Not visible from the front.
+% \begin{macrocode}
+\newcommand{\rrSF}{\@rr{SF}}
+\newcommand{\SquareSF}{\@tlen\@SquareLetter{\rrSF}\@tlen}
+\newcommand{\rrhSF}{\raisebox{-0.25mm}{\SquareSF}}
+\newcommand{\RubikSF}{\raisebox{\@hRubik}{\SquareSF}}
+\newcommand{\textRubikSF}{\rrhSF}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrSFp}
+%  \begin{macro}{\rrhSFp}
+%  \begin{macro}{\RubikSFp}
+%  \begin{macro}{\textRubikSFp}
+%  These commands  draw forms of the  SFp opposite slice rotation.
+%  We need to just make square with SFp in square; 
+%  adjust box height using a \cmd{\rule};
+%  adjust \cmd{\fboxsep} (default=3pt);
+%  adjust \cmd{\fboxrule} (default=0.4pt);
+%  bounded by \{\} so no need to reset to defaults.
+% Not visible from the front.
+% \begin{macrocode}
+\newcommand{\rrSFp}{\@rrp{SF}}
+\newcommand{\SquareSFp}{\@tlen\@SquareLetter{\rrSFp}\@tlen}
+\newcommand{\rrhSFp}{\raisebox{-0.25mm}{\SquareSFp}}
+\newcommand{\RubikSFp}{\raisebox{\@hRubik}{\SquareSFp}}
+\newcommand{\textRubikSFp}{\rrhSFp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+% 
+%
+%  \subsubsection{\hspace{3mm}Rotations SB and SBp}
+%   
+% SB = Bs is not visible from the front, so is represented in a square box.
+% Both rotating in the B direction
+% We use Bs and Bsp as the templates.
+%
+%  \begin{macro}{\rrSB}
+%  \begin{macro}{\rrhSB}
+%  \begin{macro}{\RubikSB}
+%  \begin{macro}{\textRubikSB}
+%  These commands  draw forms of the  SB opposite slice rotation.
+%  We need to just make square with SB in square; 
+%  adjust box height using a \cmd{\rule};
+%  adjust \cmd{\fboxsep} (default=3pt);
+%  adjust \cmd{\fboxrule} (default=0.4pt);
+%  bounded by \{\} so no need to reset to defaults.
+% Not visible from the front.
+% \begin{macrocode}
+\newcommand{\rrSB}{\@rr{SB}}
+\newcommand{\SquareSB}{\@tlen\@SquareLetter{\rrSB}\@tlen}
+\newcommand{\rrhSB}{\raisebox{-0.25mm}{\SquareSB}}
+\newcommand{\RubikSB}{\raisebox{\@hRubik}{\SquareSB}}
+\newcommand{\textRubikSB}{\rrhSB}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\rrSBp}
+%  \begin{macro}{\rrhSBp}
+%  \begin{macro}{\RubikSBp}
+%  \begin{macro}{\textRubikSBp}
+%  These commands  draw forms of the  SBp opposite slice rotation.
+%  We need to just make square with SBp in square; 
+%  adjust box height using a \cmd{\rule};
+%  adjust \cmd{\fboxsep} (default=3pt);
+%  adjust \cmd{\fboxrule} (default=0.4pt);
+%  bounded by \{\} so no need to reset to defaults.
+% Not visible from the front.
+% \begin{macrocode}
+\newcommand{\rrSBp}{\@rrp{SB}}
+\newcommand{\SquareSBp}{\@tlen\@SquareLetter{\rrSBp}\@tlen}
+\newcommand{\rrhSBp}{\raisebox{-0.25mm}{\SquareSBp}}
+\newcommand{\RubikSBp}{\raisebox{\@hRubik}{\SquareSBp}}
+\newcommand{\textRubikSBp}{\rrhSBp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%
+%    \subsection{\hspace{3mm}Axis rotations (textRubik versions)}
+%     \label{sec:codetextrubikaxisversions}
+%
+%  For completeness we include a \cmd{\textRubik} version of all the 
+% axis rotation codes (making them equal to their hieroglyphic \cmd{\rrh} version).
+% Obviously this list must go at the end of this file. While these commands are perhaps 
+% strictly unnecessary, the motivation is to allow users to include them in
+% a \cmd{\ShowSequence} command when using the \cmd{\textRubik} font argument.  
+%
+% \begin{macrocode}
+\newcommand{\textRubikx}{\rrhx}
+\newcommand{\textRubikxp}{\rrhxp}
+\newcommand{\textRubiky}{\rrhy}
+\newcommand{\textRubikyp}{\rrhyp}
+\newcommand{\textRubikz}{\rrhz}
+\newcommand{\textRubikzp}{\rrhzp}
+\newcommand{\textRubikl}{\rrhl}
+\newcommand{\textRubikr}{\rrhr}
+\newcommand{\textRubiku}{\rrhu}
+\newcommand{\textRubikd}{\rrhd}
+\newcommand{\textRubikf}{\rrhf}
+\newcommand{\textRubikb}{\rrhb}
+\newcommand{\textRubikLc}{\rrhLc}
+\newcommand{\textRubikLcp}{\rrhLcp}
+\newcommand{\textRubikRc}{\rrhRc}
+\newcommand{\textRubikRcp}{\rrhRcp}
+\newcommand{\textRubikUc}{\rrhUc}
+\newcommand{\textRubikUcp}{\rrhUcp}
+\newcommand{\textRubikDc}{\rrhDc}
+\newcommand{\textRubikDcp}{\rrhDcp}
+\newcommand{\textRubikFc}{\rrhFc}
+\newcommand{\textRubikFcp}{\rrhFcp}
+\newcommand{\textRubikBc}{\rrhBc}
+\newcommand{\textRubikBcp}{\rrhBcp}
+\newcommand{\textRubikCL}{\rrhCL}
+\newcommand{\textRubikCLp}{\rrhCLp}
+\newcommand{\textRubikCR}{\rrhCR}
+\newcommand{\textRubikCRp}{\rrhCRp}
+\newcommand{\textRubikCU}{\rrhCU}
+\newcommand{\textRubikCUp}{\rrhCUp}
+\newcommand{\textRubikCD}{\rrhCD}
+\newcommand{\textRubikCDp}{\rrhCDp}
+\newcommand{\textRubikCF}{\rrhCF}
+\newcommand{\textRubikCFp}{\rrhCFp}
+\newcommand{\textRubikCB}{\rrhCB}
+\newcommand{\textRubikCBp}{\rrhCBp}
+%    \end{macrocode}
+%
+%
+%
 % --------------------------
 %    End of this package
 % --------------------------
diff --git a/Master/texmf-dist/source/latex/rubik/rubikcube.ins b/Master/texmf-dist/source/latex/rubik/rubikcube.ins
index a50acb88fd4..80a62849b26 100644
--- a/Master/texmf-dist/source/latex/rubik/rubikcube.ins
+++ b/Master/texmf-dist/source/latex/rubik/rubikcube.ins
@@ -5,21 +5,7 @@
 %%  Authors: RWD Nickalls (dick@nickalls.org) 
 %%          and Apostolos Syropoulos (asyropoulos@yahoo.com)
 %%
-%%  VERSION 3.0  September 25, 2015
-%%  Copyright 2015  RWD Nickalls + A Syropoulos
-%% 
-%%
-%% This work may be distributed and/or modified under the
-%% conditions of the LaTeX Project Public License, either
-%% version 1.3c of this license or (at your option) any 
-%% later version: <http://www.latex-project.org/lppl.txt>
-%%
-%% This work consists of the files listed in the README file.
-%%
-%% This file will generate fast loadable files and documentation
-%% driver files from the doc files in this work when run through
-%% LaTeX.
-%%
+%%  
 %% --------------- start of docstrip commands ------------------
 %%
 \def\batchfile{rubikcube.ins}
@@ -31,8 +17,9 @@
   Authors: RWD Nickalls (dick@nickalls.org) 
           and Apostolos Syropoulos (asyropoulos@yahoo.com)
 
-  Copyright 2015  RWD Nickalls and A Syropoulos
+  Copyright  03 March 2017  RWD Nickalls and A Syropoulos
 
+  VERSION 4.0
 
   This work may be distributed and/or modified under the
   conditions of the LaTeX Project Public License, either
diff --git a/Master/texmf-dist/source/latex/rubik/rubikexamples.bat b/Master/texmf-dist/source/latex/rubik/rubikexamples.bat
new file mode 100644
index 00000000000..b16f8146e4c
--- /dev/null
+++ b/Master/texmf-dist/source/latex/rubik/rubikexamples.bat
@@ -0,0 +1,3 @@
+ pdflatex  --shell-escape  rubikexamples.tex
+
+
diff --git a/Master/texmf-dist/source/latex/rubik/rubikpatterns.dtx b/Master/texmf-dist/source/latex/rubik/rubikpatterns.dtx
new file mode 100644
index 00000000000..a6711d471ea
--- /dev/null
+++ b/Master/texmf-dist/source/latex/rubik/rubikpatterns.dtx
@@ -0,0 +1,540 @@
+% \iffalse meta-comment
+%
+% rubikpatterns.dtx
+%
+% version 4.0
+%
+% Authors: RWD Nickalls (dick@nickalls.org) 
+%        and Apostolos Syropoulos (asyropoulos@yahoo.com)
+%
+% Copyright   03 March 2017  RWD Nickalls + A Syropoulos
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either
+% version 1.3c of this license or (at your option) any
+% later version. The latest version of this licence is in 
+%
+%       http://www.latex-project.org/lppl.txt
+%
+%<*readme>
+%
+% The rubikpatterns package provides a collection of LaTeX commands and macros 
+% for the typesetting of Rubik cube configurations and rotation 
+% sequences using the TikZ graphic language.
+%
+% Please report errors or suggestions for improvement to
+%
+%         Dick Nickalls or Apostolos Syropoulos
+%
+% This package requires the basic TikZ package to be loaded already
+%</readme>
+%
+%<*driver>
+\listfiles
+\documentclass{ltxdoc}
+\IfFileExists{rubikpatterns.sty}{\usepackage{rubikpatterns}}{%
+    \GenericWarning{rubikpatterns.dtx}{Package file rubikpatterns.sty not found.
+    Documentation will be messed up!^^J
+    (Generate rubikpatterns.sty by (La)TeXing rubikpatterns.ins, and then^^J
+    process rubikpatterns.dtx again)^^J}\stop
+}%
+%
+\usepackage{ifpdf}
+\usepackage{url,path}  %% for references and paths
+\usepackage{graphicx}  %% for the two pdf figs
+\usepackage{hypdoc}    %% for pdf bookmarks + hyperref documenting of packages
+%%\OnlyDescription
+\EnableCrossrefs
+\PageIndex
+\CodelineIndex
+\CodelineNumbered
+\RecordChanges
+\setcounter{StandardModuleDepth}{1}
+\begin{document}
+  \DocInput{rubikpatterns.dtx}
+  \PrintChanges
+  \PrintIndex
+\end{document}
+%</driver>
+% \fi
+%
+%
+% 
+%%% \CheckSum{187}
+%
+%%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
+%%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
+%%   Asterisk      \*     Plus          \+     Comma         \,
+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+%
+%
+%
+% \title{%
+%       \ifpdf\pdfbookmark[1]{Title}{Title}\else\fi%
+%       The \textsc{rubikpatterns} package}
+%
+% \author{
+%      RWD Nickalls (dick@nickalls.org) \\
+%     A Syropoulos (asyropoulos@yahoo.com)
+%       }
+%  \date{This file describes version \RPfileversion\ (\RPfiledate)\\
+%  \texttt{www.ctan.org/pkg/rubik}}
+%  \maketitle
+%
+%  \begin{abstract}
+%  The \rubikpatterns\ package is a small data-base of well-known named 
+%  Rubik patterns and associated rotation sequences, for use  in conjunction 
+%  with the \textsc{rubikcube} and \textsc{rubikrotation} packages. It is part 
+%  of the Rubik `bundle'.
+%  \end{abstract}
+%
+%
+%  \tableofcontents
+%
+% \pagebreak
+%
+% \section{Introduction}
+%
+% The \textsc{rubikpatterns}  package is a small a data-base of well-known  Rubik 
+%  rotation sequences  for use  in  conjunction with the \textsc{rubikcube} 
+%  and \textsc{rubikrotation} packages. 
+% These sequences, which are well-known and  widely available, were  sourced from the Rubik-related
+%  websites  of Reid M and Kociemba H (see References for URLs). 
+%
+%
+%
+%   \subsection{Installation}
+%
+%  Place the file \texttt{rubikpatterns.zip} into a temporary directory, and unzip it. 
+% This will generate the following files:
+%\begin{quote}
+% \begin{verbatim}
+% rubikpatterns.ins
+% rubikpatterns.dtx
+% rubikpatterns.pdf     --this document
+% rubikpatternsLIST.tex
+% rubikpatternsLIST.pdf
+%\end{verbatim}
+%\end{quote}
+% The package documentation is the file \texttt{rubikpatterns.pdf}.
+%  The  style option \texttt{rubikpatterns.sty} is generated  by  running (pdf)\LaTeX\ on  
+% the file \texttt{rubikpatterns.ins}  as follows:
+%\begin{quote}
+%\begin{verbatim}
+%   pdflatex  rubikpatterns.ins 
+%\end{verbatim}
+%\end{quote}
+% The documentation file (\texttt{rubikpatterns.pdf}) is then generated using the following 
+% sequence of steps\,\footnote{Since the documentation includes a complicated indexing 
+% system as well a \textsc{pdf} index and hyperef links (the package \texttt{hypdoc}
+%  is used), then a lot of pdflatex runs are required. Prior to the first run it is
+% a good idea to delete any relevant \texttt{.toc}, \texttt{.aux}, \texttt{.out} files.}:
+%\begin{quote}
+% \begin{verbatim}
+%  pdflatex    rubikpatterns.dtx
+%  pdflatex    rubikpatterns.dtx
+%  makeindex -s gind.ist  rubikpatterns
+%  makeindex -s gglo.ist -o rubikpatterns.gls  rubikpatterns.glo
+%  pdflatex    rubikpatterns.dtx
+%  pdflatex    rubikpatterns.dtx
+%\end{verbatim}
+%\end{quote}
+%
+%
+% 
+%  \subsubsection{Placing the files}
+% \label{sec:placingfiles}
+%
+% Place the files either in a working directory, or where your system 
+% will find them, e.g.,~in your \texttt{/texmf-local/} directory tree. 
+% For example, on a Linux platform with a standard \TeX\ Directory Structure (TDS), then:
+%
+%\medskip
+%{\noindent}*.sty  $\rightarrow$  \texttt{/usr/local/texlive/texmf-local/tex/latex/rubik/}
+%{\newline}*.pdf  $\rightarrow$  \texttt{/usr/local/texlive/texmf-local/doc/rubik/}
+%
+%\medskip
+%
+%\medskip
+%{\noindent}\textsc{file database}:\ \ Finally, (depending on your system) update the 
+% \TeX\ file database. 
+% For example, on a Linux platform  this is achieved using the \texttt{texhash} command.
+%
+%
+%
+%       \subsection{Usage}
+% \label{sec:usage}
+% Load the  packages \textsc{rubikcube}, 
+%  \textsc{rubikrotation} and \textsc{rubikpatterns} in the \TeX\ file preamble  \textit{after} loading 
+% the TikZ package; for example, as follows: 
+%\begin{quote}
+% \begin{verbatim}
+% \usepackage{tikz}
+% \usepackage{rubikcube,rubikrotation,rubikpatterns}
+%\end{verbatim}
+%\end{quote}
+% Since the sequence macros made available  by this package are accessed using commands 
+% provided by the \textsc{rubikcube} and \textsc{rubikrotation} packages, please read the 
+% documentation of these  packages.
+%
+%
+% 
+%   \section{Rubik patterns}
+%
+% A Rubik pattern  is the configuration generated by a sequence of rotations 
+% (or `moves') from some initial starting configuration (typically a `solved' 
+% configuration). For example, `sixspot' is a well known pattern  generated  
+% from a solved Rubik cube by the  rotation sequence  
+% \texttt{U,Dp,R,Lp,F,Bp,U,Dp}, as follows:
+%
+% \bigskip
+%
+% \noindent\begin{minipage}{\textwidth}
+% \centering
+% \ifpdf
+%   \includegraphics[height=3cm]{rubikpatterns-doc-figA.pdf}
+% \else
+% \fi
+% \end{minipage}
+%
+% \bigskip
+%
+% {\noindent}The code for the above image is as follows:
+%
+%\begin{verbatim}
+% \noindent\hfil%
+% \RubikCubeSolvedWB% 
+% \ShowCube{2.4cm}{0.6}{\DrawRubikCubeRU}%
+% \RubikRotation{\SixSpot}%
+% \quad\SequenceBraceA{sixspot}{\ShowSequence{}{\Rubik}{\SequenceLong}}\quad%
+% \ShowCube{2.4cm}{0.6}{\DrawRubikCubeRU}%
+% \hfil%
+%\end{verbatim}
+%
+% \bigskip
+%
+% Note that the  appearance of a pattern generated by  a given 
+% rotation sequence is, of course, sensitive  to (a)~the particular colour 
+% configuration of the solved cube used, and (b)~the initial  orientation of 
+% the Rubik cube.
+% 
+% 
+% Consequently the appearance generated  by a given sequence
+% may appear  slightly different from 
+% that on some websites, although the  colour configuration (pattern's \textit{geometry})   
+% will, of course, be the same  (isomorphic). You may therefore need 
+% to adjust the pre- (and possibly the post-)  x,y,z rotations in 
+% order to obtain  a particular configuration as displayed elsewhere.
+%
+%
+%  \subsection{Sequence macros}
+%
+% Each of the  rotation sequences of `patterns'  made available by the 
+% \textsc{rubikpatterns} package is defined in  the file \texttt{rubikpatterns.sty}  
+% in the following  compact macro form.
+% For~example, the rotation sequence associated with the pattern known 
+% as `SixSpot' (shown in the figure above) is defined as follows:
+%\begin{verbatim}
+%\newcommand{\SixSpot}{[SixSpot],U,Dp,R,Lp,F,Bp,U,Dp,<(8q*, 8f*)>}
+%\newcommand{\sixspot}{\SixSpot}
+%\end{verbatim}
+% The macro name is \verb!\SixSpot! (the lower-case version \verb!\sixspot! can also be used). 
+% Note that the second argument which 
+% includes the  rotation sequence, also includes the pattern name in 
+% square brackets \verb![SixSpot]!  as the first element in the sequence.
+% Additional metadata (held by the macro \verb!\SequenceInfo!) is appended 
+% in angle brackets (separated by a comma) as follows: \verb!<(8q*, 8f*)>!.
+% For  details see  the \textsc{rubikrotation} package documentation.
+%
+%
+%
+%   \subsection{List of macros}
+%
+% The following is a list of the macro names of all the Rubik patterrns supplied by
+% the \textsc{rubikpatterns} package.  Note that for convenience each macro-name listed
+% has an equivalent lower-case version. See the companion file \texttt{rubikpatternsLIST.pdf}
+% for a detailed list  showing  each pattern  and its associated 
+% sequence\,\footnote{We show all these images in a separate
+% file (\texttt{rubikpatternsLIST.pdf}) purely because  generating them requires 
+% using the \LaTeX\ command-line  option \texttt{--shell-escape} in conjunction 
+% with the \textsc{rubikrotation} package.}. 
+%
+%  All the pattern names encoded here (as macros) are  well-known and widely available. 
+% However, some pattern names have been slightly modified
+% in order to avoid spaces and to keep them as similar to the original as possible.
+% On finding different sequences which generate the same pattern, then the  
+% shortest  sequence has been selected   (they can be readily distinguished by their metadata).
+% 
+% Finally, we note that there is a serious need for a standardised one-word nomenclature 
+% in order to  avoid confusion, and to facilitate computerisation and an electronic database.
+% Such a notation also needs to accommodate  those sequence variations which generate the same pattern.
+% We welcome suggestions and/or help for improvement.
+
+%
+%\begin{verbatim}
+%  \PonsAsinorum
+%  \CheckerboardsThree
+%  \CheckerboardsSix
+%  \Stripes
+%  \CubeInCube
+%  \CubeInCubeInCube
+%  \ChristmasCross
+%  \PlummersCross
+%  \Anaconda
+%  \Python
+%  \BlackMamba
+%  \GreenMamba
+%  \FemaleRattlesnake
+%  \MaleRattlesnake
+%  \FemaleBoa
+%  \MaleBoa
+%  \FourSpot
+%  \SixSpot
+%  \OrthogonalBars
+%  \SixTs
+%  \SixTwoOne
+%  \ExchangedPeaks
+%  \TwoTwistedPeaks
+%  \FourTwistedPeaks
+%  \ExchangedChickenFeet
+%  \TwistedChickenFeet
+%  \ExchangedRings
+%  \TwistedRings
+%  \EdgeHexagonTwo
+%  \EdgeHexagonThree
+%  \TomParksPattern
+%  \RonsCubeInCube
+%  \TwistedDuckFeet
+%  \ExchangedDuckFeet
+%  \Superflip
+%\end{verbatim}
+%
+% Note that  the particular  superflip sequence made available by this package 
+% (shown in \texttt{rubikpatternsLIST.pdf}) is due to  Reid (1995), and is detailed 
+% on the Kociemba webpage  \texttt{http://www.kociemba.org/math/oh.htm}. Indeed, this was the 
+% first sequence to define the `20-move' (HTM) upper boundary for solving a Rubik cube 
+% (see  Rokicki \textit{et~al.}, 2013). 
+%
+% The superflip configuration is also significant  since it is its own inverse. 
+% For example, the following two \verb!\RubikRotation! commands will generate the same 
+% configuration (starting from a solved cube):
+%\begin{verbatim}
+% \RubikRotation{\superflip}
+% \RubikRotation{\superflip,<inverse>}
+%\end{verbatim}
+% This property  is shown as  one of the examples in the Rubik bundle  file \texttt{rubikexamples.pdf}.
+%
+%
+%
+%     \section{Change history}
+%
+% \begin{itemize}
+%
+% \item Version 4.0 (March 2017)
+%
+% --- First release of this package.
+%
+% \end{itemize}
+%
+%
+%
+%   \section{References}
+%     \label{sec:references}
+%
+%\begin{itemize}
+%
+% \item Fridrich website (Fridrich J). 
+% See the `Pretty patterns'  webpage \url{http://www.ws.binghamton.edu/fridrich/ptrns.html}
+%
+% \item  Kociemba website (Kociemba H).  \url{http://www.kociemba.org/cube.htm}
+% {\newline}---for superflip see: \url{http://www.kociemba.org/math/oh.htm}
+%
+% \item Randelshofer website (Randelshofer W).  Pretty patterns. 
+% \url{http://www.randelshofer.ch/rubik/patterns/U080.01.html}
+%
+% \item Reid M. \  Patterns.  \url{http://www.cflmath.com/Rubik/patterns.html}
+%
+% \item Reid M. (1995). Superflip requires 20 face turns. (January 1995) 
+%   \url{http://www.math.ucf.edu/~reid/Rubik/CubeLovers/} 
+%  (see Section~\ref{sec:superflip})  
+% {\newline}[cited from Rokicki \textit{et~al.}, 2013]. 
+% {\newline}(Note: easier to use is the following html indexed version of the 
+% archive of the Cube-Lovers usenet group (1982--1997)  
+% \url{http://www.math.rwth-aachen.de/~Martin.Schoenert/Cube-Lovers/})
+%
+%  \item Rokicki T, Kociemba H, Davidson M and Dethridge J (2013). The diameter of the Rubik's 
+%  cube is twenty.  \textit{SIAM.\ J.\ Discrete Math.}, \textbf{27}, 1082--1105. 
+%   \url{http://tomas.rokicki.com/rubik20.pdf}
+%
+%\end{itemize}
+% 
+%
+%
+%
+% ^^A ==================================================
+% \StopEventually{\PrintIndex}
+%
+%
+%
+%        \section[The code]{The code (\texttt{rubikpatterns.sty})} 
+%
+% 
+%   \subsection{Package heading}
+%   \label{sec:CodePackageHeading}
+%
+%    \begin{macrocode}
+%<*rubikpatterns>
+\def\RPfileversion{4.0}%
+\def\RPfiledate{2017/03/03}%
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{rubikpatterns}[\RPfiledate\space (v\RPfileversion)]
+%    \end{macrocode}
+%
+%
+%    \begin{macro}{\rubikpatterns}
+% First we create a suitable logo
+%    \begin{macrocode}
+\newcommand{\rubikpatterns}{\textsc{rubikpatterns}}
+%    \end{macrocode}
+%    \end{macro}
+%
+%   \subsection{Patterns}
+%   \label{sec:patternscode}
+%
+%
+%
+%
+%  \subsubsection{Superflip}
+%   \label{sec:superflip}
+%
+% This particular superflip sequence is from the Kociemba website (his Oh webpage). 
+% It is due to  Reid (1995).
+%  \begin{macrocode}
+\newcommand{\Superflip}{[Superflip],Dp,R2,Fp,D2,F2,U2,Lp,R,Dp,R2,B,F,Rp,%
+U2,Lp,F2,Rp,U2,Rp,Up,<(20f*)>}%
+\newcommand{\superflip}{\Superflip}
+%    \end{macrocode}
+%
+%
+%  \subsubsection{Reid data}
+%
+% These named sequences are derived from the Reid website. 
+%  \begin{macrocode}
+\newcommand{\PonsAsinorum}{[PonsAsinorum],F2,B2,R2,L2,U2,D2,<(12q*, 6f*)>}%
+\newcommand{\ponsasinorum}{\PonsAsinorum}%
+\newcommand{\CheckerboardsThree}%
+{[CheckerboardsThree],F,B2,Rp,D2,B,R,U,Dp,R,Lp,Dp,Fp,R2,D,F2,Bp,<(20q*, 16f*), order 3>}%  
+\newcommand{\checkerboardsthree}{\CheckerboardsThree}%
+\newcommand{\CheckerboardsSix}%
+{[CheckerboardsSix],R2,L2,U,B,L2,Dp,F,B2,R,Lp,Fp,B,R,D,F2,Lp,Up,<(17f*, 22q), order 6>}%  
+\newcommand{\checkerboardssix}{\CheckerboardsSix}%
+\newcommand{\Stripes}{[Stripes],F,U,F,R,L2,B,Dp,R,D2,L,Dp,B,R2,L,F,U,F,<(20q*, 17f*)>}%  
+\newcommand{\stripes}{\Stripes}%
+\newcommand{\CubeInCube}{[CubeInCube],F,L,F,Up,R,U,F2,L2,Up,Lp,B,Dp,Bp,L2,U,<(18q*, 15f*)>}%  
+\newcommand{\cubeincube}{\CubeInCube}%
+\newcommand{\CubeInCubeInCube}%
+{[CubeInCubeInCube],Fp,U,Bp,Rp,U,F2,U2,Fp,Up,F,U2,D,Bp,Dp,R2,B2,Up,<(17f*, 22q)>}%  
+\newcommand{\cubeincubeincube}{\CubeInCubeInCube}%
+\newcommand{\ChristmasCross}{[ChristmansCross],U,F,Bp,L2,U2,L2,Fp,B,U2,L2,U,<(16q*, 11f*)>}%  
+\newcommand{\christmascross}{\ChristmansCross}%
+\newcommand{\PlummersCross}%
+{[PlummersCross],R2,Lp,D,F2,Rp,Dp,Rp,L,Up,D,R,D,B2,Rp,U,D2,<(20q*, 16f*)>}%  
+\newcommand{\plummerscross}{\PlummersCross}%
+\newcommand{\Anaconda}{[Anaconda],L,U,Bp,Up,R,Lp,B,Rp,F,Bp,D,R,Dp,Fp,<(14q*, 14f*)>}%  
+\newcommand{\anaconda}{\Anaconda}%
+\newcommand{\Python}{[Python],F2,Rp,Bp,U,Rp,L,Fp,L,Fp,B,Dp,R,B,L2,<(16q*, 14f*)>}%  
+\newcommand{\python}{\Python}%
+\newcommand{\BlackMamba}{[BlackMamba],R,D,L,Fp,R,Lp,D,Rp,U,Dp,B,Up,Rp,Dp,<(14q*, 14f*)>}%  
+\newcommand{\blackmamba}{\BlackMamba}%
+\newcommand{\GreenMamba}{[GreenMamba],R,D,R,F,Rp,Fp,B,D,Rp,Up,Bp,U,D2,<(14q*, 13f*)>}%    
+\newcommand{\greenmamba}{\GreenMamba}%
+\newcommand{\FemaleRattlesnake}%
+{[FemaleRattlesnake],U2,Dp,L2,D,B,U,Bp,Rp,L2,U2,F,Up,F,R,<(18q*, 14f*)>}%  
+\newcommand{\femalerattlesnake}{\FemaleRattlesnake}%
+\newcommand{\MaleRattlesnake}%
+{[MaleRattlesnake],Rp,Fp,U,Fp,U2,R,L2,B,Up,Bp,Dp,L2,U2,D,<(18q*, 14f*)>}%  
+\newcommand{\malerattlesnake}{\MaleRattlesnake}%
+\newcommand{\FemaleBoa}{[FemaleBoa],R,Up,R2,U2,F,D2,R2,Up,Dp,R,Dp,Fp,<(16q*, 12f*)>}%  
+\newcommand{\femaleboa}{\FemaleBoa}%
+\newcommand{\MaleBoa}{[MaleBoa],F,D,Rp,U,D,R2,D2,Fp,U2,R2,U,Rp,<(16q*, 12f*)>}%  
+\newcommand{\maleboa}{\MaleBoa}%
+\newcommand{\FourSpot}{[FourSpot],F2,B2,U,Dp,R2,L2,U,Dp,<(12q*, 8f*)>}%  
+\newcommand{\fourspot}{\FourSpot}%
+\newcommand{\SixSpot}{[SixSpot],U,Dp,R,Lp,F,Bp,U,Dp,<(8q*, 8f*)>}%  
+\newcommand{\sixspot}{\SixSpot}%
+\newcommand{\OrthogonalBars}%
+{[OrthogonalBars],F,Rp,U,L,Fp,Lp,F,Up,R,U,Lp,Up,L,Fp,<(14q*, 14f*)>}%  
+\newcommand{\orthogonalbars}{\OrthogonalBars}%
+\newcommand{\SixTs}{[SixTs],F2,R2,U2,Fp,B,D2,L2,F,B,<(14q*, 9f*)>}% 
+\newcommand{\sixts}{\SixTs}%
+\newcommand{\SixTwoOne}{[SixTwoOne],U,B2,D2,L,Bp,Lp,Up,Lp,B,D2,B2,<(15q*, 11f*)>}%  
+\newcommand{\sixtwoone}{\SixTwoOne}%
+\newcommand{\ExchangedPeaks}%
+{[ExchangedPeaks],F2,R2,D,R2,U,D,F2,Dp,Rp,Dp,F,L2,Fp,D,R,Up,<(16f*, 21q)>}%  
+\newcommand{\exchangedpeaks}{\ExchangedPeaks}%
+\newcommand{\TwoTwistedPeaks}%
+{[TwoTwistedPeaks],F,D2,B,R,Bp,Lp,F,Dp,L2,F2,R,Fp,Rp,F2,Lp,Fp,<(16f*, 20q)>}%
+\newcommand{\twotwistedpeaks}{\TwoTwistedPeaks}%
+\newcommand{\FourTwistedPeaks}%
+{[FourTwistedPeaks],Up,D,B,Rp,F,R,Bp,Lp,Fp,B,L,F,Rp,Bp,R,Fp,Up,D,<(18q*, 18f*)>}%
+\newcommand{\fourtwistedpeaks}{\FourTwistedPeaks}%
+\newcommand{\ExchangedChickenFeet}%
+{[ExchangedChickenFeet],F,Lp,Dp,Bp,L,F,U,Fp,Dp,F,L2,Bp,Rp,U,L2,Dp,F,<(19q*, 17f*)>}%
+\newcommand{\exchangedchickenfeet}{\ExchangedChickenFeet}%
+\newcommand{\TwistedChickenFeet}%
+{[TwistedChickenFeet],F,Lp,D,Fp,Up,B,U,F,Up,F,Rp,F2,L,Up,Rp,D2,<(18q*, 16f*)>}%
+\newcommand{\twistedchickenfeet}{\TwistedChickenFeet}%
+\newcommand{\ExchangedRings}%
+{[ExchangedRings],F,U,Dp,Lp,B2,L,Up,D,F,U,R2,L2,Up,L2,F2,<(15f*, 20q)>}%
+\newcommand{\exchangedrings}{\ExchangedRings}%
+\newcommand{\TwistedRings}%
+{[TwistedRings],F,D,Fp,D2,Lp,Bp,U,L,D,R,U,Lp,Fp,U,L,U2,<(18q*, 16f*)>}%
+\newcommand{\twistedrings}{\TwistedRings}%
+\newcommand{\EdgeHexagonTwo}%
+{[EdgeHexagonTwo],U,B2,Up,Fp,Up,D,Lp,D2,L,U,Dp,F,Dp,L2,B2,Dp,<(20q*, 16f*) order2>}% 
+\newcommand{\edgehexagontwo}{\EdgeHexagonTwo}%
+\newcommand{\EdgeHexagonThree}%
+{[EdgeHexagonThree],F,L,B,U,L,F2,B2,Rp,F2,B2,Up,Bp,Lp,Fp,<(14f*, 18q) order 3>}%
+\newcommand{\edgehexagonthree}{\EdgeHexagonThree}%
+\newcommand{\TomParksPattern}%
+{[TomParksPattern],L,U,F2,R,Lp,U2,Bp,U,D,B2,L,F,Bp,Rp,L,Fp,R,<(20q*, 17f*)>}%
+\newcommand{\tomparkspattern}{\TomParksPattern}%
+\newcommand{\RonsCubeInCube}%
+{[RonsCubeInCube],L2,D2,Lp,D2,B2,L2,B2,Lp,D2,L2,B2,Lp,B2,<(13f*, 23q)>}%
+\newcommand{\ronscubeincube}{\RonsCubeInCube}%
+\newcommand{\TwistedDuckFeet}%
+{[TwistedDuckFeet],F,Rp,B,R,U,Fp,Lp,Fp,U2,Lp,Up,D2,B,Dp,F,Bp,U2,<(20q*, 17f*)>}%
+\newcommand{\twistedduckfeet}{\TwistedDuckFeet}%
+\newcommand{\ExchangedDuckFeet}%
+{[ExchangedDuckFeet],U,F,R2,Fp,Dp,R,U,B2,U2,Fp,R2,F,D,B2,R,Bp,<(21q*, 16f*)>}%
+\newcommand{\exchangedduckfeet}{\ExchangedDuckFeet}%
+%    \end{macrocode}
+% --------------------------
+%    End of this package
+% --------------------------
+%    \begin{macrocode}
+%</rubikpatterns>
+%    \end{macrocode}
+%
+%
+%
+%
+% \Finale
+%
+\endinput
+
+
+
+
+
diff --git a/Master/texmf-dist/source/latex/rubik/rubikpatterns.ins b/Master/texmf-dist/source/latex/rubik/rubikpatterns.ins
new file mode 100644
index 00000000000..9260827909b
--- /dev/null
+++ b/Master/texmf-dist/source/latex/rubik/rubikpatterns.ins
@@ -0,0 +1,65 @@
+%% rubikpatterns.ins 
+%%
+%% version 4.0
+%%
+%% --- automatic overwriting of .sty is disabled-------
+%%  =========================================================
+%%
+%% --------------- start of docstrip commands ------------------
+%%
+\def\batchfile{rubikpatterns.ins}
+\input docstrip.tex
+
+\preamble
+
+----------------------------------------------------------------- 
+  Authors: RWD Nickalls (dick@nickalls.org) 
+          and Apostolos Syropoulos (asyropoulos@yahoo.com)
+
+  Copyright  March 03, 2017     RWD Nickalls and A Syropoulos
+
+  VERSION 4.0
+
+  This work may be distributed and/or modified under the
+  conditions of the LaTeX Project Public License, either
+  version 1.3c of this license or (at your option) any 
+  later version: <http://www.latex-project.org/lppl.txt>
+
+  This work consists of the files listed in the README file.
+----------------------------------------------------------------- 
+
+  This is a LaTeX/TikZ package for drawing Rubik cubes
+  Please report errors or suggestions for improvement to
+
+         RWD Nickalls  (dick@nickalls.org)
+         Apostolos Syropoulos (asyropoulos@yahoo.com)
+
+ This package requires the basic TikZ package to be loaded already
+------------------------------------------------------------------
+\endpreamble
+
+\keepsilent  %%disables most of the screen output
+%% \askforoverwritefalse  %%enables automatic overwriting of .sty 
+\generate{\file{rubikpatterns.sty}{\from{rubikpatterns.dtx}{rubikpatterns}}}
+
+%%now write a screen message for the user
+\obeyspaces
+\Msg{*******************************************************}
+\Msg{*                                                     *}
+\Msg{* To finish the installation you have to move the     *}
+\Msg{* following file into a directory searched by TeX:    *}
+\Msg{*                                                     *}
+\Msg{*       rubikpatterns.sty                             *}
+\Msg{*                                                     *}
+\Msg{* To produce the documentation run the file           *}
+\Msg{* rubikpatterns.dtx through LaTeX.                    *}
+\Msg{* For an index, process any filename.idx  file by     *}
+\Msg{*      makeindex -s gind.ist filename                 *}
+\Msg{* For list of changes, process any filename.glo file  *}
+\Msg{* makeindex -s gglo.ist -o filename.gls filename.glo  *}
+\Msg{*                                                     *}
+\Msg{* Happy TeXing!                                       *}
+\Msg{*******************************************************}
+
+\endbatchfile
+%%------------EOF---------------
diff --git a/Master/texmf-dist/source/latex/rubik/rubikpatternsLIST.bat b/Master/texmf-dist/source/latex/rubik/rubikpatternsLIST.bat
new file mode 100644
index 00000000000..a8e9b92cd13
--- /dev/null
+++ b/Master/texmf-dist/source/latex/rubik/rubikpatternsLIST.bat
@@ -0,0 +1,3 @@
+ pdflatex  --shell-escape  rubikpatternsLIST.tex
+
+
diff --git a/Master/texmf-dist/source/latex/rubik/rubikrotation.dtx b/Master/texmf-dist/source/latex/rubik/rubikrotation.dtx
index 57302ac37a7..2b554ef7128 100644
--- a/Master/texmf-dist/source/latex/rubik/rubikrotation.dtx
+++ b/Master/texmf-dist/source/latex/rubik/rubikrotation.dtx
@@ -1,12 +1,12 @@
 % \iffalse meta-comment
 % rubikrotation.dtx
 %
-% version 3.0
+% version 4.0
 %
-% Authors: RWD Nickalls (dick@nickalls.org) 
+% Authors:   RWD Nickalls (dick@nickalls.org) 
 %        and Apostolos Syropoulos (asyropoulos@yahoo.com)
 
-% Copyright  25 September 2015  RWD Nickalls + A Syropoulos
+% Copyright   03 March 2017  RWD Nickalls + A Syropoulos
 %
 % This work may be distributed and/or modified under the
 % conditions of the LaTeX Project Public License, either
@@ -58,7 +58,7 @@
 %
 %
 % 
-% \CheckSum{310}
+%%% \CheckSum{322}
 %
 %%% \CharacterTable
 %%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
@@ -78,7 +78,9 @@
 %
 %
 %
-% \title{The \rubikrotation\ package}
+% \title{%
+%       \ifpdf\pdfbookmark[1]{Title}{Title}\else\fi%
+%       The \rubikrotation\ package}
 %
 % \author{
 %      RWD Nickalls (dick@nickalls.org) \\
@@ -91,49 +93,49 @@
 %  \begin{abstract}
 %  The \rubikrotation\ package is a dynamic extension for  the 
 %  \textsc{rubikcube} package (both are part of the Rubik `bundle'). 
-%  The package provides  the \cmd{\RubikRotation} command which 
+%  This package provides  the \cmd{\RubikRotation} command which 
 %  processes a sequence of Rubik rotation moves on-the-fly (using the Perl script
 %  \texttt{rubikrotation.pl}), and returns the new Rubik cube  state (configuration).  
-%  The \rubikrotation\ package  also provides a command for implementing some basic 
-%  checking of the Rubik cube state (\cmd{\CheckRubikState}), and one 
-%  for  displaying any errors (\cmd{\ShowRubikErrors}).
-%
-%   The \rubikrotation\  package requires access to the \TeX\ \texttt{write18} 
-%  facility, which is enabled by using the \texttt{--shell-escape} command-line switch.
-%  The~\rubikrotation\ package has been road-tested  on a Microsoft 
-%  platform (with MiKTeX and Strawberry Perl),  on a Linux platform 
-%  (Mandriva using {\TeX}Live), and on  a Solaris platform (OpenIndiana).
+%  The \rubikrotation\ package  also provides  commands for saving the cube state 
+%  to a file (\cmd{\SaveRubikState}), and for displaying any 
+%  errors (\cmd{\ShowRubikErrors}).
 %  \end{abstract}
-%
+% 
+% 
 % \begin{minipage}{11cm}
 % \centering
 % \ifpdf
-%  \includegraphics[width=10cm]{Rubikrot-doc-figD.pdf}
+%  \strut\hspace{6mm}\includegraphics[width=10cm]{rubikrot-doc-figD.pdf}
 % \else
 % \fi
 % \end{minipage}
+% 
 %
 % \vspace{-1\baselineskip}
 %
 %  \tableofcontents
 %
+% \pagebreak
+%
 % \section{Introduction}
 %
 % The \rubikrotation\ package is a dynamic extension to the \textsc{rubikcube} package.
 % It consists of a style option (\texttt{rubikrotation.sty}), a 
-%  Perl script  (\texttt{rubikrotation.pl}) and some examples.
+%  Perl script  (\texttt{rubikrotation.pl}).
 % 
 % The primary role of the \rubikrotation\ package is to  implement  a sequence of 
-%  Rubik rotation moves on-the-fly using the \cmd{\RubikRotation} command.  Consequently, this 
-% package requires  the use of the \texttt{--shell-escape} switch to allow 
-% command-line control of  the  Perl script, which is really the `engine' of this package.
+%  Rubik rotation moves on-the-fly using the \cmd{\RubikRotation} command.  
+%  Consequently the \rubikrotation\  package requires access to the \TeX\ \texttt{write18} 
+%  facility, which is enabled by using the \texttt{--shell-escape} command-line switch.
+%  This allows command-line control of  the  Perl script, which is really the `engine' of 
+%  this package.
 %
 %  The \rubikrotation\ package has been road-tested  on a Microsoft 
-%  platform (with MiKTeX and Strawberry Perl\,\footnote{`Strawberry Perl' 
+%  platform (MiKTeX and Strawberry Perl\,\footnote{`Strawberry Perl' 
 %  (\texttt{http://strawberryperl.com}) is a free Perl 
 %  environment for MS Windows, designed to be as close as possible to the Perl 
-%  environment of Unix/Linux systems.}), on a Linux platform (Mandriva using 
-%  {\TeX}Live), and on  a Solaris platform (OpenIndiana).
+%  environment of Unix/Linux systems.}), on a Linux platform (Debian v8.2.0,  
+%  {\TeX}Live 2016, and Perl v5.20.2), and on  a Solaris platform (OpenIndiana).
 %
 % The following  commands are made available  by  \texttt{rubikrotation.sty}:
 % \begin{quote}
@@ -142,6 +144,10 @@
 %    \SaveRubikState
 %    \CheckRubikState
 %    \ShowRubikErrors
+%    \SequenceName
+%    \SequenceInfo
+%    \SequenceShort
+%    \SequenceLong
 %\end{verbatim}
 % \end{quote}
 %
@@ -164,21 +170,15 @@
 % rubikrotation.pdf     --this document
 % rubikrotation.pl      --Perl script
 % rubikrotationPL.pdf   --documentation of rubikrotation.pl
-% rubikrotation.1       --the man file
-% Rubikrot-doc-figA.pdf
-% Rubikrot-doc-figB.pdf
-% Rubikrot-doc-figC.pdf
-% Rubikrot-doc-figD.pdf
-% examples.tex
-% examples.pdf
-% examples.sh
-% examples.bat
+% rubikrotation.1       --manual file for rubikrotation.pl (`man' file)
+% rubikrot-doc-figA.pdf
+% rubikrot-doc-figB.pdf
+% rubikrot-doc-figC.pdf
+% rubikrot-doc-figD.pdf
 %\end{verbatim}
 %\end{quote}
-% Note that the package includes an  `examples' file (\texttt{examples.tex})
-% as well as associated  \texttt{.sh} (Linux) and \texttt{.bat} (Microsoft) batch 
-% files which can be used to facilitate processing  the file. 
 % The main package documentation is the file \texttt{rubikrotation.pdf}.
+% The documentation of the Perl program \texttt{rubikrotation.pl} is the file \texttt{rubikrotationPL.pdf} 
 %
 %  The  style option \texttt{rubikrotation.sty} is generated  by  running (pdf)\LaTeX\ on  
 % the file \texttt{rubikrotation.ins}  as follows:
@@ -189,7 +189,7 @@
 %\end{quote}
 % The documentation file (\texttt{rubikrotation.pdf}) is then generated using the following 
 % sequence of steps\,\footnote{Since the documentation includes a complicated indexing 
-% system as well a \textsc{pdf} index and hyperef links (the package \texttt{hypdoc}
+% system as well as an index and hyperef links (the package \texttt{hypdoc}
 %  is used), then a lot of pdflatex runs are required. Prior to the first run it is
 % a good idea to delete any relevant \texttt{.toc}, \texttt{.aux}, \texttt{.out} files.}:
 %\begin{quote}
@@ -232,7 +232,7 @@
 % file is named \texttt{rubikrotation.cfg}.
 %
 %\medskip
-%{\noindent}\textsc{the `man' file}:\ \ On a Linux platform   this file 
+%{\noindent}\textsc{the `man' file}:\ \ On a Linux platform this manual file 
 % (\texttt{rubikrotation.1}) would be  typically  located in the 
 % directory \verb!/usr/share/man/man1!.
 %
@@ -251,7 +251,7 @@
 %\end{quote}
 % which should generate something like the following:
 % \begin{verbatim}
-% This is rubikrotation version 3.0
+% This is rubikrotation version 4.0
 %       Usage: rubikrotation [-h] -i <input file> [-o <out file>]
 %       where,
 %       [-h]    gives this help listing
@@ -264,27 +264,31 @@
 %
 %       \section{Usage}
 % \label{sec:usage}
-% Load the  packages \texttt{rubikcube.sty} 
-% and \texttt{rubikrotation.sty} in the \TeX\ file preamble  \textit{after} loading 
-% the TikZ package (both Rubik packages require the TikZ package), for example, as follows: 
+% Load the  packages \texttt{rubikcube.sty}, 
+%  \texttt{rubikrotation.sty} and \texttt{rubikpatterns.sty} in the \TeX\ file 
+%  preamble  \textit{after} loading the TikZ package (all the  Rubik packages 
+%  require the TikZ package); for example, as follows: 
 %\begin{quote}
 % \begin{verbatim}
 % \usepackage{tikz}
-% \usepackage{rubikcube,rubikrotation}
+% \usepackage{rubikcube,rubikrotation,rubikpatterns}
 %\end{verbatim}
 %\end{quote}
-% and run (pdf)\LaTeX\ using the \texttt{--shell-escape} command-line switch 
+% and run (pdf)\LaTeX\ using the \texttt{--shell-escape} command-line option 
 % (see the following section).
 %
 %
+%
 %   \subsection{Enabling the \TeX\ `shell' facility}
+%   \label{sec:shellescape}
 %
-%  In order to enable the  \TeX\  `write18' facility (so it can run the Perl script) 
-% it is necessary to invoke (pdf)\LaTeX\ using the \texttt{--shell-escape} switch 
-%  as follows:
+%  In order to access the  \TeX\  \cmd{\write18} syntax (so we can access system commands, 
+%  and hence run the Perl script), 
+% it is necessary to invoke  the \LaTeX\ engine (e.g.,~(pdf)\LaTeX\  or Lua\LaTeX) 
+% using the \texttt{--shell-escape} command-line option; for example: 
 %\begin{quote}
 % \begin{verbatim}
-% pdflatex  --shell-escape   filename.tex
+% pdflatex  --shell-escape  filename.tex
 %\end{verbatim}
 %\end{quote}
 % In practice, it is probably most convenient to  run this command via a 
@@ -298,34 +302,18 @@
 % acroread filename.pdf &
 %\end{verbatim}
 %\end{quote}
-%
-%
-%   \subsection{Test file}
-%
-% An example  tex file (which demonstrates the use of some of the package commands) 
-% is   included in the package, namely:
-%\begin{quote}
-% \begin{verbatim}
-% example-rot.tex   (shows 8 worked examples)
-%\end{verbatim}
-%\end{quote}
-% This file  needs to be run using  \texttt{--shell-escape} switch; for example:
-%\begin{quote}
-% \begin{verbatim}
-% pdflatex  --shell-escape  example-rot.tex
-%\end{verbatim}
-%\end{quote}
-% Batch files (\texttt{.sh} for Linux, and \texttt{.bat} for Microsoft) are also provided 
-% to facilitate running the `example' file.
-% For example, on a Linux platform one would run a \texttt{bash} file as follows:
+%  If the \LaTeX\ engine is  Lua\LaTeX, e.g.,
 %\begin{quote}
 % \begin{verbatim}
-% bash  example-rot.sh
+% lualatex  --shell-escape  filename.tex
 %\end{verbatim}
 %\end{quote}
-% If processing this  file gives unexpected results (e.g.,~the cubes appear not to 
-% have experienced any rotations) check-out the  associated log file to see if 
-%  the operating system  had any difficulties finding files etc.
+%then  \texttt{rubikrotation.sty} will automatically load 
+%  the recently developed  \textsf{shellesc} package in order to facilitate system access to  Perl 
+%  (see Section~\ref{sec:CodePackageHeading}). See \textit{\LaTeX\ News}, issue~24, 
+%  Feb~2016 for further details of the \textsf{shellesc} package.
+%  Consequently, if you intend to use Lua\LaTeX\ then you will need to ensure your system
+%  has access to the \textsf{shellesc} package (it can always be downloaded from CTAN directly).
 %
 %
 %   \subsection{Configuration-file}
@@ -350,9 +338,9 @@
 % The configuration-file is essentially a convenient software vehicle for feeding  
 % additional  \LaTeX\ code  to the  style option \texttt{rubikrotation.sty}, and hence 
 % allows the contents of some commands to be easily adjusted and/or fine-tuned.
-% For~the \rubikrotation\ package there are two particular commands we may wish to adjust.
-% The~first is that  defining the filename of the Perl script, namely  
-% \cmd{\rubikperlname}. The second is that defining the command-line call, 
+% For~the \rubikrotation\ package there are two particular macros we may wish to adjust.
+% The~first is that  holding the filename of the Perl script, namely  
+% \cmd{\rubikperlname}. The second is that holding the command-line call, 
 % namely  \cmd{\rubikperlcmd}.
 % The~default definitions in \texttt{rubikrotation.sty}  (which assume the Perl 
 % script is executable), are as follows:  (they are detailed in 
@@ -364,8 +352,8 @@
 %                     -i rubikstate.dat -o rubikstateNEW.dat}
 %\end{verbatim}
 %\end{quote}
-% Note the need here to use the \cmd{\space} command  on the end of the backslash 
-% command  (\cmd{\rubikperlname}) in  order to force a following 
+% Note the need here (in the second macro) to use  \cmd{\space} on the end of 
+%   (\cmd{\rubikperlname}) in  order to force a following 
 % space---i.e.,~before the  first command-line argument. The following examples 
 % illustrate how the configuration-file may be used.
 %
@@ -374,7 +362,8 @@
 % a slightly modified  Perl script  
 % with the  working (executable) name \texttt{rubikrotationR77}. In this case we 
 % simply  create, in the local working  directory, a plain-text configuration-file 
-% (called \texttt{rubikrotation.cfg})  which contains just the following line:
+% (it \textit{must} be named exactly \texttt{rubikrotation.cfg})  and contains just 
+% the following line:
 %\begin{quote}
 %\begin{verbatim}
 %\renewcommand{\rubikperlname}{rubikrotationR77}
@@ -387,7 +376,8 @@
 % Now, in this particular case  we  will need to run the script using a 
 % slightly different  command, namely,
 % {\linebreak}\texttt{perl  rubikrotationR55.pl ...}, and consequently we 
-% need to  implement both these  changes in the configuration-file, as follows:
+% need to  implement \textit{both} these  changes (of name and  command) in 
+% the configuration-file,  as follows:
 %\begin{quote}
 %\begin{verbatim}
 %\renewcommand{\rubikperlname}{rubikrotationR55.pl}
@@ -395,8 +385,11 @@
 %                     -i rubikstate.dat   -o rubikstateNEW.dat}
 %\end{verbatim}
 %\end{quote}
-%{\noindent}\textsc{placing the configuration-file}:\ \ The simplest arrangement is
-% just to include the \texttt{.cfg} file in the working `test' directory.
+%{\noindent}Remember to make sure the PATH associated with the command is also correct.
+%
+%
+%{\noindent\textsc{placing the configuration-file}:\ \ The simplest arrangement is
+% just to include the \texttt{.cfg} file in the working  directory.
 % Alternatively, the \texttt{.cfg} file could be placed in the \texttt{/texmf-local/}
 % directory tree (say, in \path!/usr/local/texlive/texmf-local/tex/latex/rubik/!), 
 % but in this case one would then have to be careful to specify the 
@@ -422,7 +415,7 @@
 % \texttt{minipage} or \texttt{figure} environments
 %  generally  offers maximum  flexibility, since the effects of such commands when 
 % used inside these environments remain `local' to  the  environment, and are not 
-%  therefore accessable  outside that \textit{particular} environment 
+%  therefore accessible  outside that \textit{particular} environment 
 % (see also Section~4.1 in the \textsc{rubikcube} documentation).
 %
 %  Conversely, the only \rubikrotation\  command which should \textit{not}
@@ -430,72 +423,257 @@
 %  (see the notes on this command below). 
 % 
 %
-%   \subsection[RubikRotation command]{\cmd{\RubikRotation} command}
-% \label{sec:rubikrotationcmd}
+%
+%
+%   \subsection[RubikRotation]{\cmd{\RubikRotation} command}
+%       \label{sec:rubikrotationcmd}
 %
 %  \DescribeMacro{\RubikRotation}
-% The  \cmd{\RubikRotation}\oarg{integer}\marg{comma separated sequence}  
-% command processes  a comma separated sequence of rotations, and returns 
-% the final state.  The optional \oarg{integer} argument specifies the number
-% of times the command should be repeated.
-%
-% For example, if we wanted to see the effect of  the rotations 
-% \textbf{R, R, L, U, D} on a solved Rubik cube, we  could use the 
-% following commands. 
+% The  \cmd{\RubikRotation}\oarg{integer}\marg{comma-separated sequence}  
+% command processes  a sequence of rotation codes, and returns 
+% the final state. The inverse sequence can also be 
+% implemented (see  \textbf{Inverse} below).
+%
+%
+% The first (optional) argument \oarg{integer}  of the \cmd{\RubikRotation} command  is the number
+% of times the whole command itself should be repeated; for example
+% as follows: \verb!\RubikRotation[2]{...}!.
+%
+% The second (mandatory) argument consists of a comma-separated sequence
+% of  rotation codes, e.g.,~\texttt{U, D2}, which may be encoded as a macro. In addition, there 
+% may be additional comma-separated macros and optional \verb![name]!,  
+%  `repeat blocks' and `info blocks' (see below).  
+% The general structure of the second argument is as follows:
+% \verb!\RubikRotation{[name],...,\macro,...,(repeat)n,...,<info>}!.  
+% These elements are now described in detail.
+% 
+%
+%
+% \textbf{Square brackets}: \ This is an optional `sequence name' facility. 
+% The contents of square  brackets are not processed 
+% as rotations, and can  therefore be used  as a `name' of the sequence, e.g.,~\verb![CrossSeq]!,
+% or as a tag, to be visible in the log file. The contents must \textit{not} include commas, but 
+% can have other  separators, e.g.,~spaces, semicolons etc. Importantly, the contents of the 
+% first square bracket  will be designated the sequence name and will be held as the 
+% macro \cmd{\SequenceName}. Square brackets can also be used in repeat blocks (see below). 
+%  Square brackets must be separated by a comma from adjacent codes.
+%
+%
+% \textbf{Repeat block}: \  This is an optional comma-separated sequence of rotation
+% codes which is to be repeated a specified number of times. It must be delimited 
+% by balanced curved brackets, and an optional terminal integer $n$ (repeat number) 
+% can be used.   For example, \verb!(F,B3)2,! where the `2' indicates that the rotation 
+% sequence \verb!F,B3!  is to be processed twice. If the repeat number is omitted 
+% then $n=1$ is assumed. Repeat blocks must be separated by a comma from adjacent codes, 
+% and can include balanced square brackets (see below).
+%
+%
+% \textbf{Info block}: \ 
+% This  is an optional  block of meta information, and must be
+% delimited by  balanced  angle-brackets \verb!<..>!. An info-block  typically carries
+% information  regarding the sequence itself; typically,  something 
+% like \verb!<(20f*) //C2(a)>!. If an infoblock includes the keyword `inverse' then
+% the program will implement the inverse sequence of rotations (see below).
+% An info-block must be separated by a comma from the adjacent codes.
+% The contents of all info blocks will be held collectively as the macro \cmd{\SequenceInfo}.
+%
+%
+% \textbf{Inverse sequence}: \
+% The (mathematically) inverse sequence  of the given sequence can be implemented by including 
+% the keyword `inverse' (or INVERSE) in an infoblock, 
+% as follows \verb!\RubikRotation{<inverse>, ... }!. The keyword can be either in its 
+% own separate infoblock, or inside a larger infoblock. The program simply checks for the 
+% string `inverse',  which can be either lower-case or upper-case. The implemented sequence
+% can be checked by looking  at (or printing) the contents of the macro 
+% \cmd{\SequenceLong} (see  section on \textit{Sequence strings} below). Note that the macro 
+% \cmd{\SequenceLong} is also shown (expanded) in the log file. 
+%
+%
+% \subsubsection{Examples}
+% 
+% Some examples of the use of the \cmd{\RubikRotation} command are as follows; the commas are important and brackets must
+% be balanced and not nested:
 %\begin{quote}
 % \begin{verbatim}
-% \RubikCubeSolved   % sets up the colours for a solved cube state
-% \RubikRotation{R2,L,U,D}
-% \begin{tikzpicture}[scale=0.7]
-%    \DrawRubikCubeRU
-% \end{tikzpicture}%
+% \RubikRotation[2]{x,R2,U}   
+% \RubikRotation{\sixspot}
+% \RubikRotation{<inverse>,[myseqB],U,D,L,R2,(M,U)3,D2}  
+% \RubikRotation{[K32466],U,F,U2,F,L2,B,U2,F,Lp,Rp,F2,D,R2,U2,L2,B,Fp,
+%  L,F2,D,<(20f*) //Oh{I}>} 
+%\end{verbatim}
+%\end{quote}
+%
+% \noindent\textbf{Inverse sequence}
+%
+% Inverting a sequence involves (a)~reversing the order, and (b)~inverting each element.
+% Thus, the inverse of the sequence  \verb!(Up,D,L2,Rp)! is  \verb!(R,Lp,Lp,Dp,U)!. 
+% But~\verb!(Lp,Lp)! $\equiv$  \verb!L2!, and so the inverse 
+% of \verb!(Up,D,L2,Rp)! would generally be expressed as  \verb!(R,L2,Dp,U)!.
+% However, since the macro \cmd{\SequenceLong} records the individual elements as they are processed,
+% when a sequence is inverted notational compressions such as \verb!Lp,Lp! $\rightarrow$ \verb!L2! 
+% are not  made. 
+% For example, processing the command \verb!\RubikRotation{<inverse>,Up,D,L2,Rp}! results in the  macro 
+% \cmd{\SequenceLong}  being displayed in the subsequent  \texttt{rubikstateNEW.dat} file as
+%\begin{quote}
+% \begin{verbatim}
+% \renewcommand\SequenceLong{R,Lp,Lp,Dp,U}%
+%\end{verbatim}
+%\end{quote}
+% A more extensive example is given at the end of Section~\ref{sec:sequencestrings}.
+%
+%
+% \medskip\noindent\textbf{Repetitions}
+%
+% Repetitions can be achieved in various ways. First, all the rotations  in the second argument 
+% can be repeated  multiple times, say $n$ times, by 
+% using the optional \verb![n]! argument of the \cmd{\RubikRotation[]\{\}} command; 
+% i.e.,~the whole of the mandatory argument of the \cmd{\RubikRotation} command is then 
+% executed $n$ times.  
+%
+% Second, a sub-sequence of rotations  can be repeated within the main 
+%  argument  multiple times,  by delimiting such groups with curved brackets 
+% and a trailing integer (i.e.,~in a repeat-block), as described above.
+% If no integer is given, then $n=1$ is assumed, and hence curved brackets can also be used
+% simply to highlight particular sequences. 
+%  For example, the following five commands are equivalent:
+%\begin{quote}
+% \begin{verbatim}
+% \RubikRotation[3]{x,R2,U}
+% \RubikRotation{(x,R2,U)3}   
+% \RubikRotation{(x,R2,U)2,x,R2,U}
+% \RubikRotation{x,R2,U,x,R2,U,x,R2,U}
+% \RubikRotation{(x,R2,U),(x,R2,U),(x,R2,U)}
+%\end{verbatim}
+%\end{quote}
+%
+%
+% \medskip\noindent\textbf{Macros}
+%
+% Note also that macros representing a rotation sequence can also appear  as part of the main argument.
+% So, extending the previous example, if we were to define  \verb!\newcommand{\ShortSeq}{x,R2,U}!, then 
+% the following three commands would also be equivalent to the five previous ones:
+%\begin{quote}
+% \begin{verbatim}
+% \RubikRotation[3]{\ShortSeq}
+% \RubikRotation{(\ShortSeq)3}
+% \RubikRotation{(x,R2,U),\ShortSeq,\ShortSeq}
 %\end{verbatim}
 %\end{quote}
-%  The \cmd{\RubikRotation} command results in \LaTeX\  first writing 
+%
+%
+% \medskip\noindent\textbf{Process overview}
+%
+% The \cmd{\RubikRotation} command results in \LaTeX\  first writing 
 % the current Rubik state to a text file (\texttt{rubikstate.dat}), 
 % and then calling the Perl script \texttt{rubikrotation.pl}. The Perl 
 % script then reads the current Rubik state from the (\texttt{rubikstate.dat}) 
-% file, performs all the rotations, and then writes the new Rubik state 
-% (and any error messages) to the file \texttt{rubikstateNEW.dat}, 
-% which is then input on-the-fly by the \LaTeX\ file. This new Rubik state 
-% can then either used as the input for another \cmd{\RubikRotation}, or used
-% to generate a graphic image of the cube. 
-%
-% A given rotation sequence can be repeated multiple times, say $n$ times, by 
-% using the optional \verb![n]!. For example, the following two commands are equivalent:
+% file, performs all the rotations, and then writes the new Rubik state,
+% and the four \cmd{\Sequence...} macros (see below), and any error messages, all to the 
+% file \texttt{rubikstateNEW.dat}, 
+% which is then input on-the-fly by the \texttt{.tex} file. This new Rubik state 
+% can then be  used either as the input for another \cmd{\RubikRotation} command, or used
+% to generate a graphic image of the cube. The \cmd{\Sequence...} macros  can then
+%  be used for typesetting the sequence of rotations in various formats.
+%
+%
+%  \subsubsection{Sequence strings}
+%    \label{sec:sequencestrings}
+%
+%  \DescribeMacro{\SequenceName}
+%  \DescribeMacro{\SequenceInfo}
+%  \DescribeMacro{\SequenceShort}
+%  \DescribeMacro{\SequenceLong}
+%  The sequence of rotation codes  used as the main argument for the \cmd{\RubikRotation}
+% command is also returned in the form of four macros, namely \cmd{\SequenceName} (contains the 
+% `name' of the sequence if a \texttt{[name]} exists), \cmd{\SequenceInfo} (contains any sequence 
+%  meta data  in `info-blocks'),   \cmd{\SequenceShort} (contains the original 
+% sequence of rotation codes), and \cmd{\SequenceLong} (contains the expanded or `Long' form of the 
+% original sequence---i.e.,~in which any `short'  rotation codes (e.g.,~\texttt{R2, L3}) in the original 
+% sequence have been expanded into their separate codes---e.g.,~\texttt{R, R, L, L, L} etc.).
+%
+% For example, if we wanted to see the effect of  the sequence associated with the `SixTs'
+% cube configuration  
+% \verb![SixTs],F2,R2,U2,Fp,B,D2,L2,F,B,<(14q*,14f*)>! 
+% on a solved Rubik cube  (where `SixTs' is the `name' of the sequence),
+%  we  could use the  following commands: 
 %\begin{quote}
 % \begin{verbatim}
-% \RubikRotation[3]{x,R,U}   
-% \RubikRotation{x,R,U,x,R,U,x,R,U}
+% \RubikCubeSolved   % sets up the colours for a solved cube state
+% \RubikRotation{[SixTs],F2,R2,U2,Fp,B,D2,L2,F,B,<(14q*,14f*)>}
+% \ShowCube{2.8cm}{0.7}{\DrawRubikCubeRU}
 %\end{verbatim}
 %\end{quote}
+% Note (a)~contents of a square bracket [..] are not processed as rotations, (b)~the contents
+% of the first square bracket in a sequence is taken to be the `name' of the sequence
+%  (see Section~\ref{sec:prefixedargument}  for more details).
+% In this example the four \cmd{\Sequence..} macros described above would now hold 
+% the following strings:
+%\begin{quote}
+% \cmd{\SequenceName}  = SixTs
+%{\newline} \cmd{\SequenceInfo}  = (14q*,14f*)
+%{\newline} \cmd{\SequenceShort} = [SixTs],F2,R2,U2,Fp,B,D2,L2,F,B
+%{\newline} \cmd{\SequenceLong}  = F,F,R,R,U,U,Fp,B,D,D,L,L,F,B
+%\end{quote}
+%
+% As another example, we now show how to  implement  the inverse of the  above \verb!SixTs! 
+% sequence,  by including  the key word `inverse' in an infoblock, and, more conveniently, 
+% using the macro \verb!\sixts! from  the  \textsc{rubikpatterns} package, as follows:
+%\begin{quote}
+% \begin{verbatim}
+% \RubikRotation{<inverse>,\sixts}
+%\end{verbatim}
+%\end{quote}
+% In this case, the log file would then show the associated \cmd{\Sequence..} macros as follows:
+%\begin{quote}
+% \begin{verbatim}
+%...SequenceName = SixTs
+%...SequenceInfo = inverse; (14q*; 9f*)
+%...SequenceShort = [SixTs],F2,R2,U2,Fp,B,D2,L2,F,B
+%...SequenceLong = Bp,Fp,Lp,Lp,Dp,Dp,Bp,F,Up,Up,Rp,Rp,Fp,Fp
+%\end{verbatim}
+%\end{quote}
+% showing that the macro \cmd{\SequenceShort}  holds the \verb!\sixts! sequence, while
+%  the macro \cmd{\SequenceLong}  holds the inverse sequence which was actually implemented.
+%
+% For further details  regarding the use of these \cmd{\Sequence..} macros  for typesetting
+% the various components of a sequence, and why the \cmd{\SequenceLong} command is 
+% particularly useful, see Section~10 in the \textsc{rubikcube} documentation
+% (the \cmd{\ShowSequence} command).
+%
+%
 %
-
 %  \subsubsection{Sequences as macros}
-%   \label{sec:seq-as-macros}
+%    \label{sec:seq-as-macros}
 %
 % Macros which are arguments of the \TeX\ \cmd{\write} command are  expanded
 % on writing (Eijkhout 1992, \S\,30.2.3, p.\,238)[\,see refs Section~\ref{sec:references}\,].
 % Consequently we  are able to  use  a sequence-defining  macro as an argument for 
 % the \cmd{\RubikRotation} command. In fact this is very convenient, since it allows 
-% one to store lots of different rotation sequences by name alone.
+% one to store lots of different rotation sequences by name alone. Note that 
+% \texttt{rubikpatterns.sty} (part of the Rubik bundle)  is a collection/database 
+% of many such well-known named sequences. 
 %
-% For example, we can use the name `sixspot' for a macro denoting the rotation sequence 
+% For example, by installing the \textsc{rubikpatterns} package we  are able to use the 
+% name `sixspot' for a macro denoting the rotation sequence 
 % which generates the well known `sixspot' configuration (see the `patterns' page on the 
-%   Reid website)[\,see refs Section~\ref{sec:references}\,], as follows:
+%   Reid website)[\,see refs Section~\ref{sec:references}\,]. The `sixspot' sequence is 
+% defined as follows:
 %\begin{quote}
 % \begin{verbatim}
-% \newcommand{\sixspot}{U,Dp,R,Lp,F,Bp,U,Dp}
+% \newcommand{\sixspot}{U,Dp,R,Lp,F,Bp,U,Dp,<(8q*, 8f*)>}
 %\end{verbatim}
 %\end{quote}
-% With this new \cmd{\sixspot} command we are now able to generate the graphic (sixspot cube) 
+% Armed with the \cmd{\sixspot} macro we are now able to generate the graphic (sixspot cube) 
 % very easily using the following code---this time we demonstrate the use of the more convenient
 %  \cmd{\ShowCube} command (which includes the \texttt{tikzpicture} environment):
 %
 % \medskip
 %
-% \begin{minipage}{6cm}
+% \begin{minipage}{7cm}
 % \begin{verbatim}
+% \usepackage{rubikcube,rubikrotation}
+% \usepackage{rubikpatterns}
+% ...
 % \RubikCubeSolved
 % \RubikRotation{\sixspot}
 % \ShowCube{3cm}{0.7}{\DrawRubikCubeRU}
@@ -504,7 +682,7 @@
 % \begin{minipage}{3.4cm}
 % \centering
 % \ifpdf
-%   \includegraphics[height=3cm]{Rubikrot-doc-figA.pdf}
+%   \includegraphics[height=3cm]{rubikrot-doc-figA.pdf}
 % \else
 % \fi
 % \end{minipage}
@@ -515,87 +693,75 @@
 % and macros;  for example, \verb!\RubikRotation{x,y,\sixspot,x}!.
 %
 %
-%  \subsubsection{Arguments prefixed with *, [, ]}
+%  \subsubsection{Arguments  in square brackets }
 %    \label{sec:prefixedargument}
 %
-%  If any of the comma separated arguments  is prefixed with either *, [ or ] they are  
-% interpreted as an inactive `string', and not as a rotation. This feature therefore 
-% allows a string argument to be used as a label, which can be very useful.
+%  The contents of a square bracket  are not processed as rotations, but are simply  
+% interpreted as an inactive `string'. This feature therefore 
+% allows  the contents to be used as a label, which can be very useful.
+% Note the contents of square brackets must not include commas, but spaces  and semicolons 
+% are allowed.
 %
-%  For example, we can use this facility to label the   `sixspot' configuration mentioned above,
+%  For example, we can use this facility to `name' the   `SixSpot' configuration mentioned above,
 % as follows:
 %\begin{quote}
 % \begin{verbatim}
-% \RubikRotation{[sixspot],U,Dp,R,Lp,F,Bp,U,Dp}
+% \RubikRotation{[SixSpot],U,Dp,R,Lp,F,Bp,U,Dp}
 %\end{verbatim}
 %\end{quote}
 % In practice, it is quite useful to go one step further and  include 
-% the [\,] label feature  in the \cmd{\sixspot} command, as follows,
+% the [\,]  label-name feature  in the \cmd{\sixspot} command, as follows,
 %\begin{quote}
 % \begin{verbatim}
-% \newcommand{\sixspot}{[sixspot],U,Dp,R,Lp,F,Bp,U,Dp}
+% \newcommand{\sixspot}{[SixSpot],U,Dp,R,Lp,F,Bp,U,Dp}
 %\end{verbatim}
 %\end{quote}
-% since this has the great  advantage of making the label-name visible in the log file.
-% For example, the following command, which uses the rotations \textbf{x}, \textbf{x}  
-% and \textbf{y} to  initially rotate the `solved' cube before applying 
-% the `sixspot' sequence  of rotations,
+% Note that using the \texttt{[name]} facility has the great advantage of making the 
+% label-name visible in the log-file.
+% For example, the following command, which uses the rotations \textbf{x2},
+% and \textbf{y} to   rotate the Rubik cube after applying 
+% the `sixspot' sequence  of rotations:
 %\begin{quote}
 % \begin{verbatim}
-% \RubikRotation{x2,y,\sixspot}
+% \RubikRotation{\sixspot,x2,y}
 %\end{verbatim}
 %\end{quote}
 % will then be represented in the log file as 
 %\begin{quote}
 % \begin{verbatim}
-% ...command=rotation,x2,y,[sixspot],U,Dp,R,Lp,F,Bp,U,Dp
-% ...arguments passed to `rotation' sub = x2 y [sixspot] U Dp R Lp F ...
-% ...rotation x OK (= rrR + rrSr + rrLp)
-% ...rotation x OK (= rrR + rrSr + rrLp)
-% ...rotation y OK (= rrU + rrSu + rrDp)
-% ...[sixspot] is a label OK
-% ...rotation U OK
-% ...rotation Dp OK 
-% ...rotation R OK
-% ...rotation Lp OK
-% ...rotation F OK
-% ...rotation Bp OK
-% ...rotation U OK
-% ...rotation Dp OK 
+% ...dataline = rotation,[SixSpot],U,Dp,R,Lp,F,Bp,U,Dp,<(8q*; 8f*)>,x2,y
+% ...[SixSpot] is a label OK
+% ...rotation U, OK
+% ...rotation Dp, OK 
+% ...rotation R, OK
+% ...rotation Lp, OK
+% ...rotation F, OK
+% ...rotation Bp, OK
+% ...rotation U, OK
+% ...rotation Dp, OK 
+% ...Expanding x2 ...
+% ...rotation x, OK (= x = R + Sr + Lp)
+% ...rotation x, OK (= x = R + Sr + Lp)
+% ...rotation y, OK (= y = U + Su + Dp)
+% ...writing new Rubik state to file rubikstateNEW.dat
+% ...SequenceName = SixSpot
+% ...SequenceInfo = (8q*; 8f*)
+% ...SequenceShort = [SixSpot],U,Dp,R,Lp,F,Bp,U,Dp,x2,y
+% ...SequenceLong = U,Dp,R,Lp,F,Bp,U,Dp,x,x,y
 %\end{verbatim}
 %\end{quote}
-% In this way, several named rotation sequences can be easily distinguished
-% in the log file from  adjacent  rotation sequences.
+% Note that the \verb!\sixspot! macro, as held in the \textsc{rubikpatterns} package, includes  a terminal 
+% infoblock holding the  `SequenceInfo' as indicated in the  above example.
+%
+% Also, note that the square bracket feature allows for several named rotation sequences 
+% to be  easily distinguished in the log file from  adjacent  rotation sequences.
 % This feature is also useful when typesetting a sequence of rotation codes, since the first
 % element will then appear in the form \verb![name]!, obviating the need to typeset the 
 % name of the sequence separately. 
 %
-% To this end, the  
-% \verb!ForEachX! macro---from the \verb!forarray!  package---can be very useful.
-% For example, this macro is central to the following example macro for typesetting
-%  a  rotation  sequence using the Rubik \cmd{\rr} command:
-%\begin{quote}
-%\begin{verbatim}
-%\def\x{\thislevelitem}
-%\def\xcount{\thislevelcount}
-%
-%\newcommand{\showseq}[1]{%
-%  \ForEachX{,}{%
-%    \ifthenelse{\xcount=1}{\texttt{\x}}{,\ \rr{\x}}%
-%    }{#1}.
-%}
-%\end{verbatim}
-%\end{quote}
-% Now, for a  sequence defined as |\newcommand{\myseq}{[myseq],U,D,Lwp,R}|, then
-%  the command |\showseq{\myseq}| will result in the following output:
-%\begin{quote}
-% \texttt{[myseq]},\ \textbf{U},\ \textbf{D},\ \textbf{Lwp},\ \textbf{R}.
-%\end{quote}
-% Note that we are able to  typeset the name \texttt{[myseq]} differently from the 
-% remaining sequence  since the counter \verb!\xcount! allows us to locate the first item.
-% However, this macro as it stands needs further development in order to handle 
-% sequence elements with a terminal digit (e.g.,~\texttt{R2})---the macro will need 
-% to first  expand this to \texttt{R, R} if  the Rubik commands are to be used.
+% See also the \cmd{\ShowSequence} command (in the \textsc{rubikcube} package)
+% for a convenient way of displaying a sequence of rotations in various formats.
+%
 %
 %   \subsubsection{Groups}
 %
@@ -604,7 +770,8 @@
 % of groups and subgroups.
 %  For~example, using the \rubikrotation\ package it is easy to 
 % show that three cycles of the `sixspot' sequence return the Rubik cube to its 
-% original state. More formally this is equivalent to  $($\cmd{\sixspot}$)3 \equiv 0$,
+% original state. More formally this is equivalent to
+%  $($\cmd{\sixspot}$)3 \equiv e$\,\footnote{$e$ is the `identity' element},
 %  and can  be nicely  illustrated  by implementing the following pseudocode:
 %\begin{verbatim}
 % \RubikCubeSolved . \RubikRotation[3]{\sixspot} = \RubikCubeSolved   
@@ -613,7 +780,7 @@
 % \begin{minipage}{11cm}
 % \centering
 % \ifpdf
-%  \includegraphics[width=10cm]{Rubikrot-doc-figC.pdf}
+%  \includegraphics[width=10cm]{rubikrot-doc-figC.pdf}
 % \else
 % \fi
 % \end{minipage}
@@ -623,30 +790,31 @@
 %
 %  The \cmd{\RubikRotation} command  can also be used to  scramble the 
 % cube using a random sequence of rotations. If  the first argument 
-% is the lowercase word `random' \textsc{and} the second argument 
+% is the lower-case word `random' \textsc{and} the second argument 
 % is an integer $n$, ($1\leq n \leq 200$), then a random sequence 
 % of $n$ rotations will be performed; otherwise  a default value 
 % of 50 is used (for example, if the second argument is not an integer). 
 % If $n > 200$ then  the currently set maximum value $n=200$ will be used.
 %
-% As a safety feature the  maximum $n$ can be changed only by editing  the 
-% set value of  the Perl variable \verb!$maxn! in the Perl script 
-% \texttt{rubikrotation.pl},  where (see line~583)  we  currently have
+%  As a safety feature the  maximum $n$ can be changed only by editing  the 
+%  set value of  the Perl variable \verb!$maxn! in the Perl script 
+%  \texttt{rubikrotation.pl},  where we  currently have
+%  (see  the `random' subroutine in the document \texttt{rubikrotationPL.pdf})
 %\begin{quote}
 %\begin{verbatim}
 % my $maxn=200;
 %\end{verbatim}
 %\end{quote}
 %
-% For example, the following commands will scramble a solved cube using a 
+% For example, the following commands scramble a solved cube using a 
 % sequence of 120 random rotations, and display the state in the form of 
-%  a  semi-flat cube. 
+%  a  semi-flat (SF) cube. 
 %
 
 % \begin{minipage}{3.4cm}
 % \centering
 % \ifpdf
-%   \includegraphics[height=4cm]{Rubikrot-doc-figB.pdf}
+%   \includegraphics[height=4cm]{rubikrot-doc-figB.pdf}
 % \else
 % \fi
 % \end{minipage}
@@ -655,7 +823,7 @@
 %\begin{verbatim}
 % \RubikCubeSolved%
 % \RubikRotation{random,120}%
-% \ShowCube{5.5cm}{0.5}{\DrawRubikCubeFlat}
+% \ShowCube{5.5cm}{0.5}{\DrawRubikCubeSF}
 %\end{verbatim}
 % \end{minipage}
 %
@@ -691,7 +859,7 @@
 %\begin{quote}
 %\begin{verbatim}
 % \RubikCubeSolved%
-% \RubikRotation{*sixspot,U,Dp,R,Lp,F,Bp,U,Dp}%
+% \RubikRotation{U,Dp,R,Lp,F,Bp,U,Dp}%
 % \SaveRubikState{sixspot.tex}%
 %\end{verbatim}
 %\end{quote}
@@ -709,12 +877,12 @@
 % \RubikFaceBack{B}{B}{B}{B}{R}{B}{B}{B}{B}%
 %\end{verbatim}
 %\end{quote}
-% We can therefore access and draw this configuration later, when required, 
-% simply by inputting  the file as follows:
+% We can therefore access and draw this configuration in a Semi-Flat  format 
+% later, when required,  simply by inputting  the file as follows:
 %\begin{quote}
 %\begin{verbatim}
 %\input{sixspot.tex} 
-%\ShowCube{7cm}{0.7}{\DrawRubikCubeFlat}
+%\ShowCube{7cm}{0.7}{\DrawRubikCubeSF}
 %\end{verbatim}
 %\end{quote}
 %
@@ -724,7 +892,7 @@
 %  \DescribeMacro{\CheckRubikState}
 %  Since it is easy to inadvertently define an invalid Rubik cube 
 % (e.g.,~enter an invalid number of, say, yellow facelets), this command 
-%  checks the current colour state of all the cubies
+%  simply checks the current colour state of all the cubies
 % of a 3x3x3 Rubik cube, and  shows the number of facelets  of each colour.  
 % An ERROR: code is issued if the number of facelets having a given colour exceeds~6.
 % The results are written to the the \texttt{.log} file, and displayed under 
@@ -736,7 +904,9 @@
 % \CheckRubikState%
 %\end{verbatim}
 %\end{quote}
-% Note that  such a check is implemented automatically with each \cmd{\RubikRotation} command.
+% Note (1)~that  such a check is implemented automatically with each \cmd{\RubikRotation} 
+% command, and (2)~this is actually only a very superficial check---simply counting the number 
+% of cubies of each colour.
 %
 %
 %
@@ -758,6 +928,7 @@
 % Once the document is free of errors this command can be removed or just commented out. 
 % Run the test file \texttt{example-rot.tex} to see an example of the use of this command. 
 %
+%
 %    \section{Files generated}
 %
 % 
@@ -780,21 +951,22 @@
 %
 % 
 %     \section{General overview}
-% \label{generaloverview}
-% When \LaTeX\  processes  \texttt{rubikrotation.sty}  the following steps
-% are implemented.
-% \begin{itemize}
+%   \label{generaloverview}
 %
+%  When \LaTeX\  processes  \texttt{rubikrotation.sty}  the following steps
+%  are implemented.
+% \begin{itemize}
 % 
 % \item[1.]  A check is made to see if  \texttt{fancyvrb.sty} is loaded: if not 
-% then this package  is loaded if it is available (this package is required  
-% for inputting the  file  \texttt{rubikstateERRORS.dat}).
+% then this package  is loaded  (this package supplies the command \cmd{\VerbatimInput} which 
+% is required for inputting the  file  \texttt{rubikstateERRORS.dat} in verbatim form).
 % 
 % \item[2.]  A check is made to see if a configuration-file (\texttt{rubikrotation.cfg})
 %  exists:  if so then  this file is input.
 %
-% \item[3.] The text file \texttt{rubikstateNEW.dat} is overwritten (if it exists): 
-% otherwise the file is created (this prevents an `old' file being used by \LaTeX).
+% \item[3.] The text file \texttt{rubikstateNEW.dat} is overwritten (if it exists), 
+%  otherwise the file is created (this prevents an `old' version of the file being 
+%  used by \LaTeX).
 %
 % \item[4.]  The plain-text file \texttt{rubikstateERRORS.dat} is created. 
 % This file collects error  messages generated by the Perl script.
@@ -804,14 +976,14 @@
 %
 % When a \cmd{\RubikRotation} command is processed it first  writes the current 
 % colour configuration of each face (the `rubik state') to the temporary file 
-% \texttt{rubikstate.dat} (to be read by the Perl script \texttt{rubikrotation.pl}). 
+% \texttt{rubikstate.dat} (this will be read by the Perl script \texttt{rubikrotation.pl}). 
 % The \cmd{\RubikRotation} command also appends the keyword `\texttt{checkrubik}' 
 %  as well as  a copy of the  string of Rubik rotations. 
 % It~then calls the Perl script  \texttt{rubikrotation.pl}. 
 %
 % For example, if we use the command \cmd{\RubikCubeSolved}
 % followed by the command \verb!\RubikRotation[2]{U,D,L,R}!, then the associated 
-%  \texttt{rubikstate.dat} file  would be as follows:
+%  \texttt{rubikstate.dat} file  will be written as follows:
 %\begin{quote}
 % \begin{verbatim}
 % % filename: rubikstate.dat
@@ -826,12 +998,12 @@
 % rotation,U,D,L,R
 %\end{verbatim}
 %\end{quote}
-% Note that the \cmd{\RubikRotation} option \texttt{[2]} results in the line \texttt{rotation,U,D,L,R} 
+% Note that the \cmd{\RubikRotation} option \texttt{[2]} results in the string ``\texttt{rotation,U,D,L,R}'' 
 % being written twice to the \texttt{rubikstate.dat} file, as shown above.
 %
 % Alternatively, if we used the command 
 % \verb!\RubikRotation{random, 45}! then the last line  written to the file 
-% would be the string  `\texttt{rotation,random,45}', as follows:
+% would be the string  ``\texttt{rotation,random,45}'', as follows:
 %\begin{quote}
 % \begin{verbatim}
 % % filename: rubikstate.dat
@@ -846,29 +1018,31 @@
 %\end{verbatim}
 %\end{quote}
 % A  \cmd{\CheckRubikState} command   triggers the same sequence of events except
-% no `rotation' line is written.
+% that no ``\texttt{rotation,....}'' line is written.
 %
 % The action of the Perl script  \texttt{rubikrotation.pl} is controlled by 
 % the keywords (first argument of
 % each line)  associated with each line of the file \texttt{rubikstate.dat}. 
 % When control passes to  Perl,  the script \texttt{rubikrotation.pl} starts 
-% by loading the current rubikstate (prompted by the keywords \texttt{up}, \texttt{down}, 
-% \texttt{left}, \texttt{right}, \texttt{front}, \texttt{back}, in the file 
-% \texttt{rubikstate.dat}).  Next the Perl script 
-% performs  some basic checks (prompted by the key word \texttt{checkstate}), and 
-% then it processes  the sequence of Rubik rotations (prompted by the keyword 
-% \texttt{rotation}).  If, instead, the second argument  of the `rotation' string 
-% is the keyword `random', and  provided this is followed by a valid integer, say $n$, 
+% by loading the current rubikstate (prompted by the keywords `\texttt{up}', `\texttt{down}', 
+% `\texttt{left}', `\texttt{right}', `\texttt{front}', `\texttt{back}'), and performing
+% a syntax check---significant syntax errors at this stage 
+%  will cause the program to  issue appropriate error messages and then terminate cleanly.
+% Next, the Perl script  performs  some basic cube checks 
+% (prompted by the key word `\texttt{checkstate}'), and then the program processes  
+% the sequence of Rubik rotations (prompted by the keyword 
+% `\texttt{rotation}').  If, instead, the second argument  of the `\texttt{rotation,...}' string 
+% is the keyword `\texttt{random}', and  provided this is followed by a valid integer, say $n$, 
 % then the Perl script performs  a sequence of $n$ random rotations.
-% Finally, the Perl script writes the final `rubikstate' to the text file 
+% Finally, the Perl script writes the final rubikstate to the text file 
 % \texttt{rubikstateNEW.dat}. All error messages are written to the 
-% text file \texttt{rubikstateERRORS.dat} and  also to the \LaTeX\  log file. 
+% text file \texttt{rubikstateERRORS.dat} and  also to the \LaTeX\  log-file. 
 %
 % Control then reverts to  \LaTeX\  which then inputs the file
 % \texttt{rubikstateNEW.dat}. If there are more \cmd{\RubikRotation} commands
-% then this cycle  repeats accordingly.  Eventually a \cmd{\Draw...} command 
-% of some form is  reached and the final rubikstate is drawn in a TikZ picture 
-% environment.
+% (in the \texttt{.tex} file) then this cycle  repeats accordingly.  
+% Eventually a \cmd{\Draw...} command is  reached (in the \texttt{.tex} file) and 
+% the final rubikstate is drawn in a TikZ picture  environment.
 %
 % If the TikZ picture environment is followed by a \cmd{\ShowRubikErrors} command,
 % then a `verbatim' copy of the \texttt{rubikstateERRORS.dat} file is displayed
@@ -911,13 +1085,22 @@
 % \newline\url{http://pgfplots.sourceforge.net/TeX-programming-notes.pdf}
 % {\newline}[\,re:~loop macros in Section~\ref{sec:feuersanger}\,]
 %
+%  \item Kociemba  website (Kociemba H). \url{http://www.kociemba.org/cube.htm}
 %
-% \item Nickalls RWD and Syropoulos A (2015).  The \textsc{rubikcube} package. 
+% \item Nickalls RWD and Syropoulos A (2015).  The \textsc{rubikcube} package, v3.0.
 % \newline\url{http://www.ctan.org/pkg/rubik}, 
 %
-% \item Reid M. \  Patterns.  \url{http://www.cflmath.com/Rubik/patterns.html}
-% {\newline}[\,re:~sequences as macros; in Section~\ref{sec:seq-as-macros}\,]
 %
+% \item Randelshofer website (Randelshofer W).  \url{http://www.randelshofer.ch/rubik/}
+%  \ [\,re:~sequences  and  supersetENG notation\,]
+%
+%
+% \item Reid website (Reid M). \  Patterns.  \url{http://www.cflmath.com/Rubik/patterns.html}
+% \ [\,re:~sequences as macros; in Section~\ref{sec:seq-as-macros}\,]
+%
+%
+% \item Tellechea C and Segletes SB (2016).  The  \textsf{listofitems} package, v1.2
+% \newline\url{http://www.ctan.org/pkg/listofitems}
 %\end{itemize}
 % 
 %
@@ -925,6 +1108,27 @@
 %     \section{Change history}
 %
 % \begin{itemize}
+%
+% \item Version 4.0 (March  2017)
+%
+% --- The \cmd{\RubikRotation} command has been enhanced to allow its argument to include
+%  so-called repeat-blocks (rotation-sequences which can be repeated multiple times), and 
+% info-blocks for holding sequence metadata (see Section~\ref{sec:rubikrotationcmd}).
+% Syntax checking of the \cmd{\RubikRotation} argument is much improved 
+% (see \texttt{rubikrotationPL.pdf} for details of the Perl script).
+%
+% --- Four new macros  which  hold derived data (see Section~\ref{sec:rubikrotationcmd}).
+% \begin{quote}
+%  \cmd{\SequenceName}
+%  \newline\cmd{\SequenceInfo}
+%  \newline\cmd{\SequenceShort}
+%  \newline\cmd{\SequenceLong}
+% \end{quote}
+%
+% --- Better syntax checking of the \cmd{\RubikRotation} argument by the Perl program \texttt{rubikrotation.pl}.
+%
+%
+%
 % \item Version 3.0 (25 September 2015)
 %
 % --- The \cmd{\RubikRotation} command now  actions multiple instances of its  argument 
@@ -932,7 +1136,7 @@
 % \cmd{\RubikRotation[3]\{R,x\}}  is equivalent to the  command \cmd{\RubikRotation\{R,x,R,x,R,x\}}
 % (see Sections~\ref{sec:rubikrotationcmd} and \ref{sec:rubikrotationcode}).
 %
-% --- If a comma separated  element used as an argument for the \cmd{\RubkRotation} 
+% --- If a comma separated  element used as an argument for the \cmd{\RubikRotation} 
 % command is prefixed with either a * or [ or ]  character then it is not actioned 
 % as a rotation (see Section~\ref{sec:prefixedargument}). 
 %
@@ -940,7 +1144,8 @@
 % including \texttt{-h} to show some `help'  and `usage' information 
 % (see Section~\ref{sec:placingfiles}).
 %
-% --- A `man' file  for the Perl script \texttt{rubikrotation.pl} is now included in the package.
+% --- A `man' file (manual file) for the Perl script \texttt{rubikrotation.pl} is now 
+%  included in the package.
 %
 % --- The Perl script \texttt{rubikrotation.pl} now  uses as input and output filenames
 %  those specified  in the command-line of the CALLing program. This now allows the 
@@ -964,7 +1169,7 @@
 %
 %
 %
-%        \section{The code (\texttt{rubikrotation.sty})} 
+%        \section[The code]{The code (\texttt{rubikrotation.sty})} 
 % 
 % {\noindent}In the following, the term `Perl script'  denotes the script
 %  \texttt{rubikrotation.pl}. Useful information regarding the 
@@ -973,11 +1178,12 @@
 %  Abrahams \textit{et.~al} (1990).
 % 
 %   \subsection{Package heading}
+%   \label{sec:CodePackageHeading}
 %
 %    \begin{macrocode}
 %<*rubikrotation>
-\def\RRfileversion{3.0}%
-\def\RRfiledate{2015/09/25}%
+\def\RRfileversion{4.0}%
+\def\RRfiledate{2017/03/03}%
 \NeedsTeXFormat{LaTeX2e}
 \ProvidesPackage{rubikrotation}[\RRfiledate\space (v\RRfileversion)]
 %    \end{macrocode}
@@ -994,7 +1200,7 @@
 %
 %
 %
-%  {\noindent}The \rubikrotation\  package requires access to the  fancyvrb package
+%  {\noindent}The \rubikrotation\  package requires access to the  \textsf{fancyvrb} package
 %  for the \cmd{\VerbatimInput\{\}} command  which we use for inputting and displaying
 %  the error file (see Section~\ref{sec:showrubikerrors}).
 %    \begin{macrocode}
@@ -1004,6 +1210,24 @@
    \RequirePackage{fancyvrb}}
 %    \end{macrocode}
 %
+%
+%   {\noindent}For the \cmd{\write18} syntax to work with
+%   Lua\TeX\ (so we can access system commands) we require 
+%   the recent \textsf{shellesc} package, which we load using the 
+%   \textsf{ifluatex} conditional (see Section~\ref{sec:shellescape}).
+%    \begin{macrocode}
+\@ifpackageloaded{ifluatex}{}{%
+   \typeout{---rubikrotation requires the ifluatex package.}%
+   \RequirePackage{ifluatex}}
+\ifluatex%
+   \@ifpackageloaded{shellesc}{}{%
+   \typeout{---rubikrotation requires the shellesc package
+       to run using Lua\LaTeX.}%
+   \RequirePackage{shellesc}}
+\fi%
+%    \end{macrocode}
+%
+%
 %  \medskip
 % 
 %   \subsection{Some useful commands}
@@ -1059,30 +1283,30 @@
 \newcommand{\rubikperlname}{rubikrotation}
 %    \end{macrocode}
 %    \end{macro}
-%
+% Note that here we are assuming that the script is an executable file.
 %
 %    \begin{macro}{\rubikperlcmd}
 %  This holds the command-line  code for calling the Perl script 
-%  (assumed to be an executable file). 
 %  Note that the command-line requires a mandatory  input filename preceded
 %  by the \texttt{-i}~switch. An optional output filename (preceded by the
 %  \texttt{-o}~switch) may be used, otherwise the default output filename of 
 %  \texttt{rubik-OUT.dat} will be used.
 %
-% Note that it is very important that this .sty file actually specifies an
+% Note that it is very important that we do actually specify an
 % output filename (for receiving data from the Perl script). This is because
 % (a)~The Perl script \texttt{rubikrotation.pl} is currently configured to read its 
 % output filename  as an argument from the command-line (so it can be flexibly 
 % used as a stand-alone script for processing a given Rubik state through a 
 % sequence of rotations), and (b)~\texttt{rubikrotation.sty} is currently 
-% configured to read  its input from the file \texttt{rubikstateNEW.dat}.
+% configured to read  its input (i.e.,~data  generated  by  the Perl script)
+%  from the file \texttt{rubikstateNEW.dat}.
 %    \begin{macrocode}
 \newcommand{\rubikperlcmd}{\rubikperlname\space%
                    -i rubikstate.dat   -o rubikstateNEW.dat}
 %    \end{macrocode}
-%  Remember to use the \cmd{\space} command following the \LaTeX\  backslash 
-% command in order to  generate the mandatory space between it and the first 
-% command-line argument).
+%  Remember to use the \cmd{\space} macro following the \cmd{\rubikperlname} macro 
+%  in order to  generate the mandatory space before the first 
+% command-line argument.
 %
 %  A plain-text  configuration-file \verb!rubikrotation.cfg! can be used to 
 %  change the default command-line code  using a renewcommand 
@@ -1094,7 +1318,7 @@
 %
 % If a configuration file exists (\texttt{rubikrotation.cfg}) then input it here,
 % i.e.,~\textit{after} defining the \cmd{\rubikperlname} and \cmd{\rubikperlcmd} 
-% commands and \textit{before} creating the \texttt{rubikstateERRORS.dat} file.
+% macros and \textit{before} creating the \texttt{rubikstateERRORS.dat} file.
 %    \begin{macrocode}
 \typeout{---checking for config file (rubikrotation.cfg)...}
 \IfFileExists{rubikrotation.cfg}{%
@@ -1139,7 +1363,7 @@
 \newwrite\outfile%
 \immediate\openout\outfile=rubikstateERRORS.dat%
 \@print{\@comment rubikstateERRORS.dat}%
-\@print{\@comment ---(RR.sty v\RRfileversion): comments output by Perl script}%
+\@print{\@comment --------------------}%
 \immediate\closeout\outfile%
 %    \end{macrocode}
 %
@@ -1184,7 +1408,7 @@
 % in order to trigger the Perl script to implement its \texttt{checkstate} subroutine.
 %
 % The actual state is simply an ordered sequence of the  faces and the colours 
-% associated with each facelet of that face. The colour associated with a particular facelet
+% associated with each facelet of a face. The colour associated with a particular facelet
 % is held by the variable for that facelet. For example, the top-left facelet associated with
 % the \textsc{front} face is held in the variable \cmd{\Flt} (see Section~\ref{saverubikstate}).
 % Further relevant documentation is in the \textsc{rubikcube} package. 
@@ -1256,10 +1480,12 @@
 % Perl script \texttt{rubikrotation.pl}.  It~also writes comments to the 
 % data file and also to the log file.
 %
-% In order to allow the user to (optionally)  write the main argument multiple
-% times to the output data-file, we require this command to allow an optional
+% The way we allow the user to (optionally) process the main argument multiple
+%  times  is simply by writing the associated output command multiple
+% times to the output data-file. Consequently, we require the \cmd{\RubikRotation} 
+% command to allow a square-bracket optional
 % argument (a non-negative integer) to specify the number of such repeats.
-% In order to implement an optional argument facility we use two macros 
+% In order to implement this optional argument facility we use two macros 
 % (countingloop and loopcounter) detailed by Feuers\"{a}nger (2015) 
 % [\,see refs Section~\ref{sec:references}\,]\label{sec:feuersanger}, 
 % as follows:
@@ -1286,8 +1512,9 @@
 % the command to write the main argument to the output data file.
 %    \begin{macrocode}
 \newcommand{\RubikRotation}[2][1]{%
+   \typeout{---TeX process (rubikrotation.sty)-------}% 
    \typeout{---NEW rotation command------------------}%
-   \typeout{---command = RubikRotation{#1}}%
+   \typeout{---command = RubikRotation[#1]{#2}}%
    \typeout{---writing current Rubik state to file rubikstate.dat}%
    \@openstatefile% open data file
    \@print{\@comment filename: rubikstate.dat}%
@@ -1299,14 +1526,20 @@
    \@countingloop{\ourRRcounter} in 1:{#1}{%
          \immediate\write\outfile{rotation,#2}}%
    \@closestatefile% close data file
-   \typeout{---running Perl script (rubikrotation)}%
+   \typeout{---CALLing Perl script (rubikrotation.pl)}%
    \immediate\write18{\rubikperlcmd}%
-   \typeout{---inputting NEW datafile (written by Perl script)}%
+   \typeout{---inputting NEW datafile (data written by Perl script)}%
    \input{rubikstateNEW.dat}%
    \typeout{-----------------------------------------}%
  }
 %    \end{macrocode}
 %    \end{macro}
+% Note that the new \cmd{\ShellEscape} command implemented by the recent
+% \textsf{shellesc} package is equivalent to \cmd{\immediate}\cmd{\write18} (see above),
+%  and so we  probably ought to use \cmd{\ShellEscape} instead in future (and hence load
+% \textsf{shellesc} automatically). At present, however, we leave the user to make 
+% sure that the \textsf{shellesc} package is actually  available on their system.
+% 
 %
 %
 %   \subsection{ShowRubikErrors command}
@@ -1314,11 +1547,13 @@
 %
 %    \begin{macro}{\ShowRubikErrors}
 % This command inputs the file \texttt{rubikstateERRORS.dat}.
+% Also made a more convenient synonym = \cmd{\ShowErrors}.
 %    \begin{macrocode}
 \newcommand{\ShowRubikErrors}{%
    \typeout{---ShowRubikErrors: inputting file rubikstateERRORS.dat}%
    \VerbatimInput{rubikstateERRORS.dat}%
  }
+\newcommand{\ShowErrors}{\ShowRubikErrors}
 %    \end{macrocode}
 %    \end{macro}
 %
@@ -1340,9 +1575,9 @@
    \@print{\@comment filename: rubikstate.dat}%
    \@printrubikstate% 
    \@closestatefile% close data file
-   \typeout{---running Perl script (rubikrotation)}%
+   \typeout{---running Perl script (rubikrotation.pl)}%
    \immediate\write18{\rubikperlcmd}%
-   \typeout{---inputting NEW datafile (written by Perl script)}%
+   \typeout{---inputting NEW datafile (data written by Perl script)}%
    \input{rubikstateNEW.dat}%
    \typeout{-----------------------------------------}%
  }
diff --git a/Master/texmf-dist/source/latex/rubik/rubikrotation.ins b/Master/texmf-dist/source/latex/rubik/rubikrotation.ins
index 99384f15aa4..0c2aed56982 100644
--- a/Master/texmf-dist/source/latex/rubik/rubikrotation.ins
+++ b/Master/texmf-dist/source/latex/rubik/rubikrotation.ins
@@ -1,26 +1,9 @@
 %% rubikrotation.ins 
 %%
-%% version 3.0
+%% version 4.0
 %%
 %% --- automatic overwriting of .sty is disabled-------
 %%  =========================================================
-%%  Authors: RWD Nickalls (dick@nickalls.org) 
-%%               and 
-%%           Apostolos Syropoulos (asyropoulos@yahoo.com)
-%%
-%%  Copyright  25 September 2015    RWD Nickalls + A Syropoulos
-%% 
-%%
-%% This work may be distributed and/or modified under the
-%% conditions of the LaTeX Project Public License, either
-%% version 1.3c of this license or (at your option) any 
-%% later version: <http://www.latex-project.org/lppl.txt>
-%%
-%% This work consists of the files listed in the README file.
-%%
-%% This file will generate fast loadable files and documentation
-%% driver files from the doc files in this work when run through
-%% LaTeX.
 %%
 %% --------------- start of docstrip commands ------------------
 %%
@@ -33,8 +16,9 @@
   Authors: RWD Nickalls (dick@nickalls.org) 
           and Apostolos Syropoulos (asyropoulos@yahoo.com)
 
-  Copyright 25 September 2015     RWD Nickalls and A Syropoulos
+  Copyright 03 March 2017     RWD Nickalls and A Syropoulos
 
+  VERSION 4.0
 
   This work may be distributed and/or modified under the
   conditions of the LaTeX Project Public License, either