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diff --git a/Master/texmf-dist/source/latex/rubik/rubikcube.dtx b/Master/texmf-dist/source/latex/rubik/rubikcube.dtx
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+% \iffalse meta-comment
+%
+%% rubikcube.dtx
+%% Copyright 2014  RWD Nickalls (dick@nickalls.org) and A Syropoulos (asyropoulos@yahoo.com)
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status `maintained'.
+% 
+% The Current Maintainer of this work are  RWD Nickalls and A Syropoulos
+%
+%
+% This work consists of the files rubikcube.dtx and rubikcube.ins
+% and the derived file rubikcube.sty.
+%
+%<*readme>
+%
+% The rubikcube 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{rubikcube.sty}{\usepackage{rubikcube}}{%
+    \GenericWarning{rubikcube.dtx}{Package file rubikcube.sty not found.
+    Documentation will be messed up!^^J
+    (Generate rubikcube.sty by (La)TeXing rubikcube.ins, and then^^J
+    process rubikcube.dtx again)^^J}\stop
+}%
+\usepackage{ifpdf}
+\usepackage{url}  %% for references
+\usepackage{supertabular} %% for Notation table
+%%\OnlyDescription
+\EnableCrossrefs
+\CodelineIndex
+\CodelineNumbered
+\RecordChanges
+\setcounter{StandardModuleDepth}{1}
+\begin{document}
+  \DocInput{rubikcube.dtx}
+  \PrintChanges
+  \PrintIndex
+\end{document}
+%</driver>
+% \fi
+%
+%
+% 
+% \CheckSum{3912}
+%
+%%% \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{The \textsf{rubikcube} package}
+%
+% \author{
+%      RWD Nickalls (dick@nickalls.org) \\
+%     A Syropoulos (asyropoulos@yahoo.com)
+%       }
+%  \date{This file describes version \RCfileversion, last revised \RCfiledate}
+%  \maketitle
+%
+%  \begin{abstract}
+%  The \rubikcube\ package provides LaTeX commands and macros 
+%  for  typesetting  Rubik cube (3x3x3) notation,  configurations, and 
+%  rotation sequences  using the  TikZ graphic language.
+%  \end{abstract}
+%
+% \bigskip
+% \hfil
+% \begin{minipage}{2cm}
+% \centering
+% \begin{tikzpicture}[scale=0.4]
+% \RubikFaceUpAll{W}
+% \RubikFaceFrontAll{O}
+% \RubikFaceRightAll{G}
+% \DrawRubikCubeRU
+% \end{tikzpicture}
+% \end{minipage}
+% \begin{minipage}{2cm}
+% \centering
+% \begin{tikzpicture}[scale=0.4]
+% \DrawRubikLayerFaceAll{W}
+% \DrawRubikLayerSideT {R}{R}{R}
+% \DrawRubikLayerSideLR{B}   {G}
+%                      {B}   {G}
+%                      {B}   {G}
+% \DrawRubikLayerSideB {O}{O}{O}
+% \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);
+% \end{tikzpicture}
+% \end{minipage}
+% \RubikF\RubikR\RubikU\RubikRp\RubikUp\RubikFp\
+% \ \ $\longrightarrow$
+% \begin{minipage}{2cm}
+% \centering
+% \begin{tikzpicture}[scale=0.4]
+% \DrawRubikLayerFace{W}{W}{B}
+%                    {W}{W}{O}
+%                    {W}{R}{B}
+% \DrawRubikLayerSideT {G}{G}{R}
+% \DrawRubikLayerSideLR{R}   {W}
+%                      {B}   {W}
+%                      {O}   {W}
+% \DrawRubikLayerSideB {G}{W}{O}
+% \end{tikzpicture}
+% \end{minipage}
+% \hfil
+%
+% \bigskip
+%
+%  \tableofcontents
+%
+% \pagebreak
+%
+% \section{Introduction}
+%
+% The  \rubikcube\  package   provides  a collection of \LaTeX\ commands 
+% and macros for  typesetting  Rubik cube  configurations  and layer-rotation 
+% instructions using the  PGF/TikZ graphic languages---see examples below.
+% We have extended slightly the  layer-rotation  hieroglyphic notation,  originally  
+% developed  by Garfath-Cox (1981), and improved by Duvoid (2010, 2011).
+%
+%  The \textsf{rubikcube} package has been road-tested  on a Microsoft 
+%  platform (with MikTeX and Strawberry Perl)
+%  and on a Linux platform ({\TeX}Live and Mandriva).
+%
+% 
+%  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).
+% For the mathematics and group theory associated with   Rubik's cube  see Chen (2004), 
+% Joyner (2008), Hutchings (2011),  Rokicki \textit{et al.}\ (2013). 
+% 
+%
+%  \subsection{Requirements}
+%
+%     The \rubikcube\ package requires the TikZ package.
+%
+%
+%  \subsection{Supporting tool---the \textsf{rubikrotation} package}
+%  \label{sec:addons}
+%
+%  The \textsf{rubikrotation} package, is a dynamic extension to
+% the \rubikcube\ package. It consists of  the  Perl program  
+% \texttt{rubikrotation.pl}  and style option \texttt{rubikrotation.sty}. 
+%  The \textsf{rubikrotation} package  implements rotation sequences and 
+%  random  scrambling of the 3x3x3 Rubik cube 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.
+%
+%  Since the  \cmd{\RubikRotation} command works by \textsc{call}ing the  
+%  \texttt{rubikrotation.pl} program, it follows that the \textsf{rubikrotation}
+%   package requires  (a)~Perl to be installed, 
+%  and (b)~\LaTeX\ needs to be run using the  \texttt{--shell-escape} commandline option.
+%  See the \textsf{rubikrotation}  documentation for details.
+%  The \textsf{rubikrotation} package has been road-tested  on a Microsoft 
+%  platform (with MikTeX and Strawberry Perl)
+%  and on a Linux platform ({\TeX}Live and Mandriva).
+%
+%
+%  \subsection{Copyright}
+%  Copyright 2014 RWD Nickalls and A Syropoulos.
+%
+% \medskip
+% {\noindent}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 any
+% later version. The latest version of this licence is in 
+%  http://www.latex-project.org/lppl.txt
+%
+%
+% \section{Installation}
+%
+%
+%  \subsection{Generating the 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.sty
+% rubikcube.pdf
+% example-cube.tex
+% example-cube.pdf
+% Rubik_doc_figA.pdf
+% Rubik_doc_figB.pdf
+% Rubik_doc_figC.pdf
+% Rubik_doc_figD.pdf
+% Rubik_doc_figE.pdf
+%\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}
+% The documentation file (\texttt{rubikcube.pdf}) was generated using the following
+% steps:
+% \begin{verbatim}
+%  pdflatex   rubikcube.dtx
+%  pdflatex   rubikcube.dtx
+%  makeindex -s gind.ist  rubikcube
+%  makeindex -s gglo.ist -o rubikcube.gls  rubikcube.glo
+%  pdflatex   rubikcube.dtx
+%\end{verbatim}
+%
+%
+%  \subsection{Placing the files}
+%
+% Place the files either in the local working directory, or where your system 
+% will find them. For a Linux system with a standard \TeX\ Directory Structure (TDS), then:
+%
+%\medskip
+%{\noindent}*.sty  $\rightarrow$ 
+%   \texttt{/usr/local/texlive/texmf-local/tex/latex/local/rubikcube/}
+%{\newline}*.pdf  $\rightarrow$  \texttt{/usr/local/texlive/texmf-local/doc/rubikcube/}
+%
+% \medskip
+% {\noindent}Finally, (depending on your system) update the  \TeX\ file database using the 
+% \texttt{texhash} command.
+%
+%
+% \subsection{Usage}
+%
+% Load the package by using the command \cmd{\usepackage\{rubikcube\}}.
+% Note that the \rubikcube\ package requires the TikZ package, and so always load TikZ 
+% before \rubikcube\  as follows:
+% \begin{quote}
+%\begin{verbatim}
+% \usepackage{tikz}
+% \usepackage{rubikcube}
+%\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.
+%
+%
+%    \section{TikZ picture environment}
+%
+%  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 2.10 (2012) (900 pages)
+%  \item tkz-base-screen.pdf
+%  \end{itemize}
+% An example of the TikZ picture environment for use with \rubikcube\ is as follows 
+%  If no scale is used (default scale = 1), then each of the small cubie sides 
+%  will have a length of 1~cm.
+% \begin{quote}
+%\begin{verbatim}
+% \begin{tikzpicture}[scale=0.5]
+% ....
+% \end{tikzpicture}
+%\end{verbatim}
+% \end{quote}
+% A very useful feature of  TikZ  is that it automatically 
+% minimises the surrounding  white-space, and consequently this is 
+% mostly quite sufficient.
+%
+% However,  when making complicated  side-by-side figures it is 
+% sometimes helpful to place each sub-figure in a surrounding minipage.
+% In this case, a useful approach is to  first adjust 
+% the `scale' parameter  to obtain the appropriate size, and 
+% then adjust the minipage width as necessary.
+% 
+% Note that sometimes a temporary \cmd{\fbox\{\}} can be a useful aid  when 
+% trying to  visualise the  full extent of the minipage 
+% (and its whitespace). In this case remember to include a 
+% trailing \% after the first brace \{ of the fbox command in order not to 
+% collect any extra `space', as follows:
+% \begin{quote}
+%\begin{verbatim}
+% \fbox{%
+%    \begin{minipage}{2cm}
+%    \centering
+%    \begin{tikzpicture}[scale=0.5]
+%    ....
+%    \end{tikzpicture}
+%    \end{minipage}
+% } 
+%\end{verbatim}
+% \end{quote}
+% Unexpected spacing between two adjacent images, or between an 
+% image and adjacent text, is usually related to inappropriate 
+% (and hidden) white-space associated with the image or its 
+% associated \cmd{\minipage}.
+%
+% 
+% \subsection{\rubikcube\ commands}
+%
+% Although the \rubikcube\ package has been designed with TikZ in mind, 
+% it is important to appreciate that of all the  various \rubikcube\  
+% commands only the `Draw...' commands actually have to be  used within
+% a  TikZ picture environment. 
+%
+% Indeed, using \rubikcube\ 
+% commands outside the TikZ picture environment can make for useful 
+% flexibility when a documant is generating  more than one figure
+% or image. This is because the scope of a command when used inside
+% a TikZ environment is constrained to be `local' to that particular
+%  environment, and hence its influence is  not accessable outside 
+% the environment.  
+%
+% For example,  
+%
+% \subsection{\cmd{\draw} error message}
+% \label{drawerrormessage}
+%
+% If a  \cmd{\Draw...} command is used \textit{outside} a TikZ picture
+%  environment, then \LaTeX\  issues a  \cmd{\draw} ``Undefined control
+% sequence'' error message, indicating that it is trying to draw 
+% something using an undefined TikZ \cmd{\draw} command. 
+%
+% For example, if we  try to run the \rubikcube\ command 
+%  \cmd{\DrawRubikFlat}  without a surrounding TikZ picture environment 
+%  you will see something like  the following error message.
+%\begin{verbatim} 
+%! Undefined control sequence.
+%\FlatUp ... }{#1}\pgfmathsetmacro {\uy }{#2}\draw
+%                                                  [line join=round,...
+%l.56 \DrawRubikFlat
+%\end{verbatim}
+%
+%
+%     \section{Command conventions}
+%     \label{sec:conventions}
+%
+%
+% \DescribeMacro{\rubikcube}
+% This command generates the logo \rubikcube.
+%
+%
+%   \subsection{Capital letters}
+%
+%  Each `word' in a command (except the word `text')  starts with a capital letter. 
+%  For example,  \cmd{\DrawRubikCubeRU}, \cmd{\DrawCubieRU}. 
+%  However, in line 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. How the six  face letters  are  written depends 
+% on  the command; sometimes in uppercase (eg \cmd{\rrD}, \cmd{\rrDs}, \cmd{\rrDa} ),
+%  and  sometimes in lowercase  (eg~\cmd{\rrSu}, \cmd{\rrd}, \cmd{\rrhf}).
+%
+%     \subsection{XYZ argument ordering}
+%
+% 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. 
+%
+% The convention is that the letter codes are ordered in the XYZ order; 
+% ie 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).
+%
+% \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 end of \rubikcube\ commands}
+%
+% It is important to include a trailing \% on the end of \rubikcube\ 
+% commands when used \textit{outside}  a TikZ picture environment.
+% This is to prevent  unwanted `space' characters appearing in 
+% the graphics. Note that a useful feature  of the TikZ environment
+% is that it  automatically minimises any such space.
+%
+%
+%  \section{Rubik rotation commands and notation}
+%  \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 (\url{http://www.ws.binghamton.edu/fridrich/ptrns.html}).
+% By the term \rubikcube\ we  denote only  the familiar
+% 3x3x3 puzzle cube. We  denote similar puzzle cubes  of a different size by 
+% the term  NCubes (NxNxN). 
+% 
+% It is recommended  that  commas  are used to separate sequestial 
+% Rubik moves or commands to avoid  ambiguity, especially when using just
+%  lettercodes on their own. 
+% For example, in the following sequence the commas usefully remove any ambiguity:
+%  \rrU,\rrLw2,\rrUsp,\rrDa \ \ (|\rrU,\rrLw2,\rrUsp,\rrDa|).
+%
+% 
+%
+% \subsection{Overview}
+%
+% The \rubikcube\  notation  comprises  a range of 
+% commands for moves or rotations (e.g.,~\rrR, \rry, \rrBw) and their equivalent  hieroglyphs 
+% (e.g.,~\rrhR, \rrhy, \rrhBw), 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 letter-code in a square; for example \rrhBw, \rrhSb. 
+%
+% \DescribeMacro{\rr..}
+%  The letter-code of a rotation is typeset  (as in text) using the rubik-rotation 
+%  \cmd{\rr..} stem: ie \rrR\ is typeset using the command \cmd{\rrR}. 
+% The hieroglyph of a rotation command is generated  (in text) by
+% \DescribeMacro{\rrh..}
+% using instead the stem \cmd{\rrh..}. \ Thus the command \cmd{\rrhR} generates 
+% \rrhR\  which is the hieroglyph associated with \rrR.  
+%
+% \DescribeMacro{\Rubik..}
+% A vertically combined lettercode  and its hieroglyph  is generated using the command 
+% stem \cmd{\Rubik..}. For example, \RubikR\ is generated by the command \cmd{\RubikR}, 
+% with  the square hieroglyph sitting on the baseline.
+% For some hieroglyphs,  eg~the \rrhx, \rrhy, \rrhz\ denoting 90~degree axis rotations, 
+% the only  difference between the \cmd{\rrh..} and \cmd{\Rubik..} forms is that 
+% the \cmd{\Rubik..}  form is eleveted  to sit on the baseline just like the other
+%  \cmd{\Rubik..} hieroglyphs. 
+% For example \cmd{\rrhyp} generates \rrhyp, while
+% \cmd{\Rubikyp} generates \Rubikyp.
+% 
+% \DescribeMacro{\textRubik..}
+% A horizontally combined  lettercode and its hieroglyph (in sequence as in text) 
+% is generated using  the command stem  \cmd{\textRubik..}. 
+% For example,  \textRubikR\ is typeset using the command \cmd{\textRubikR}.
+% A list of all commands and their associated  hieroglyphs is given in
+%  Section~\ref{sec:listofcommands}. 
+%
+% 
+%
+% \subsection{Face rotations}
+%
+% \DescribeMacro{\rrU}
+% \DescribeMacro{\rrD}
+% \DescribeMacro{\rrL}
+% \DescribeMacro{\rrR}
+% \DescribeMacro{\rrF}
+% \DescribeMacro{\rrB}
+% 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 (\rrF, \rrB, \rrL, \rrR, \rrU, \rrD) 
+% denotes a clockwise 90-degree rotation of the  face as shown in  
+% Figure~\ref{fig:notation}. 
+% For example, \rrD\ is generated by the `rubik rotation' command \cmd{\rrD}.
+%
+% \DescribeMacro{\rrUp}
+% \DescribeMacro{\rrDp}
+% \DescribeMacro{\rrLp}
+% \DescribeMacro{\rrRp}
+% \DescribeMacro{\rrFp}
+% \DescribeMacro{\rrBp}
+%  An appended  prime~$^\prime$ indicates an anticlockwise rotation; eg \rrFp. 
+%  This is sometimes written as  \rrF$\boldmath{^{-1}}$. The `prime' notation is 
+%  achieved by appending a lowercase `p' to the face rotation command. For example, \rrRp\ 
+%  is generated by \cmd{\rrRp}. 
+%
+% \begin{figure}[hbt]
+%  \centering
+%  \ifpdf
+%    \includegraphics[height=6cm]{Rubik_doc_figA.pdf}
+%  \fi
+% \caption{\label{fig:notation}} 
+% \end{figure}
+%
+%
+%  \subsection{Slice rotations}
+%
+% \DescribeMacro{\rrSu}
+% \DescribeMacro{\rrSd}
+% \DescribeMacro{\rrSl}
+% \DescribeMacro{\rrSr}
+% \DescribeMacro{\rrSf}
+% \DescribeMacro{\rrSb}
+% 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 
+% rotation  between the \textsc{right} and \textsc{left} faces  whose rotation 
+% direction follows the rotation \rrR\ (rotation is isomorphic to \rrR) is denoted 
+% as \rrSr, which is typeset using the command \cmd{\rrSr}. Note that in these cases
+%  the trailing  \texttt{r}  in the command  is lowercase.
+%
+% \DescribeMacro{\rrSup}
+% \DescribeMacro{\rrSdp}
+% \DescribeMacro{\rrSlp}
+% \DescribeMacro{\rrSrp}
+% \DescribeMacro{\rrSfp}
+% \DescribeMacro{\rrSbp}
+% 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  \rrSlp\ (\cmd{\rrSlp}) and 
+% \rrSr\ (\cmd{\rrSr}) are identical.
+% The equivalence is more obvious when we see their respective hieroglyphs.
+% For example, in this case \linebreak \rrSlp\ (\cmd{\rrSlp}) 
+%  $\equiv$ \rrhSlp\ (\cmd{\rrhSlP}), 
+%  and  \rrSr\ (\cmd{\rrSr}) $\equiv$ \rrhSr\ (\cmd{\rrhSr}). 
+%
+% \pagebreak
+%
+% \subsubsection*{MES slice notation}
+%
+% \DescribeMacro{\rrM}
+% \DescribeMacro{\rrE}
+% \DescribeMacro{\rrS}
+% \DescribeMacro{\rrMp}
+% \DescribeMacro{\rrEp}
+% \DescribeMacro{\rrSp}
+% An alternative and somewhat confusing (and hence is non-standard) slice notation
+%  which is sometimes used  is the following 
+% so-called MES notation,  as used in the Waterman algorithm
+%  (Treep and Waterman 1987).
+% \begin{itemize}
+% \item[\rrM] \ (\textsc{middle} slice, between the \textsc{left} 
+%      and \textsc{right} faces;  direction  follows  \rrL),
+% \item[\rrE] \  (\textsc{equator} slice, between the \textsc{up} and \textsc{down} 
+%      faces;  direction follows \rrD),
+%  \item[\rrS] \  (\textsc{standing} slice, between the \textsc{front} and 
+%      \textsc{back} faces; 
+%  direction follows \rrF).
+% \end{itemize}
+% Each of these also has a reversed (prime) version.
+% The equivalent S notations are therefore as follows:  \rrE\ $\equiv$ \rrSd, 
+% \rrEp\ $\equiv$ \rrSu, 
+% \rrM\ $\equiv$ \rrSl, \rrMp\ $\equiv$ \rrSr, \rrS\ $\equiv$ \rrSf, \rrSp\ $\equiv$ \rrSb. 
+%
+% 
+%
+% \subsubsection*{Singmaster slice notation}
+%
+% \DescribeMacro{\rrUs}
+% \DescribeMacro{\rrDs}
+% \DescribeMacro{\rrLs}
+% \DescribeMacro{\rrRs}
+% \DescribeMacro{\rrFs}
+% \DescribeMacro{\rrBs}
+% 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.
+%
+% Each of these commands denotes a  rotation of  two opposite faces 
+% in the same  direction. For example, \textRubikUs\ $\equiv$ \textRubikU\ + \textRubikDp, 
+% which is typeset as: 
+% \newline |\textRubikUs\ $\equiv$ \textRubikU\ + \textRubikDp|, 
+% i.e., for  \rrUs\ both face-rotations are in the \textit{same} direction 
+% as \rrU. 
+%
+%
+% \subsubsection*{Anti-slice notation}
+%
+% \DescribeMacro{\rrUa}
+% \DescribeMacro{\rrDa}
+% \DescribeMacro{\rrLa}
+% \DescribeMacro{\rrRa}
+% \DescribeMacro{\rrFa}
+% \DescribeMacro{\rrBa}
+% Each of these commands denotes a  rotation of  two opposite faces 
+% in \textit{opposite}  directions. 
+% For example, \textRubikUa\ $\equiv$ \textRubikU\ + \textRubikD, 
+% which is typeset as: 
+% \newline |\textRubikUa\ $\equiv$ \textRubikU\ + \textRubikD|.
+% See the link to `notation' on the `Pretty patterns' page of the 
+% Fridrich website.
+%
+%
+%      \subsection{Wide rotations}
+%
+% \DescribeMacro{\rrUw}
+% \DescribeMacro{\rrDw}
+% \DescribeMacro{\rrLw}
+% \DescribeMacro{\rrRw}
+% \DescribeMacro{\rrFw}
+% \DescribeMacro{\rrBw}
+% 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 \rrRw. 
+% Similarly, the prime $^\prime$ version \rrLwp\  is generated by \cmd{\rrLwp}.
+%
+%  The superscript~$^2$, or sometimes just an ordinary 2, indicates that the rotation
+%  is applied twice. For example \rrR\textbf{$^2$} or \rrR\textbf{2} 
+%  denote  \textit{two} successive 90~degree clockwise rotations of the \textsc{right} face.
+%
+%
+%
+%     \subsection{Axis rotations}
+%
+% \DescribeMacro{\rrx}
+% \DescribeMacro{\rry}
+% \DescribeMacro{\rrz}
+% \DescribeMacro{\rrhx}
+% \DescribeMacro{\rrhy}
+% \DescribeMacro{\rrhz}
+% Whole-cube clockwise rotations  of 90-degrees about about the orthogonal  axes centred 
+% on the  \textsc{right}, \textsc{up}, \textsc{front}  faces are denoted 
+% as \rrx, \rry, \rrz\ (the \cmd{\rr..} forms) respectively, 
+% with their hieroglyphs (the \cmd{\rrh..} forms) being denoted 
+% as \rrhx, \rrhy, \rrhz\ in order to distinguish them from  square layer-rotation 
+% hieroglyphs.
+% Note that \rrx, \rry, \rrz\ rotations are always expressed in lowercase, 
+% and hence this practice is extended also to the commands. 
+%
+% An \rrx\textbf{2} rotation (two \rrx\ rotations one after 
+% the other, ie~\rrhx\ \rrhx) 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, \rrxp\ (which is generated by appending a `p' to the end of 
+% the command, ie~\cmd{\rrxp}). 
+%
+% \DescribeMacro{\Rubikx}
+% \DescribeMacro{\Rubiky}
+% \DescribeMacro{\Rubikz}
+% These  \cmd{\Rubik..}  forms (and their prime `p' versions) generate the same
+%  hieroglyphs  as their \cmd{\rrh..} versions, except that their spacing is 
+%  similar to that associated with the `square box'  \cmd{\Rubik..}  hieroglyphs.  
+% Consequently  when typesetting  an axis command in a sequence of  `square-box' 
+% \cmd{\Rubik..} commands, it is better to use the \cmd{\Rubik..} form rather than
+% the equivalent \cmd{\rrh..} form (see the examples in Section~\ref{sec:examples}).
+% There are no \cmd{\textRubik..} forms for the axis commands (since they are 
+% not necessary).
+%
+%
+% \subsubsection*{The u, d, l, r, f, b notation} 
+%
+% \DescribeMacro{\rru}
+% \DescribeMacro{\rrd}
+% \DescribeMacro{\rrl}
+% \DescribeMacro{\rrr}
+% \DescribeMacro{\rrf}
+% \DescribeMacro{\rrb}
+% A commonly used  alternative for the \rrx, \rry, \rrz\ notation 
+% (and endorsed  by the WCA)  uses the 
+% lowercase face letter to denote a 90~degree whole-cube rotation  in the same 
+% sense as that of the   standard face rotations. 
+%
+% {\noindent}Thus  
+% \rru\ $\equiv$ \rry, \    \rrd\ $\equiv$ \rryp, \ 
+% \rrl\ $\equiv$ \rrxp, \   \rrr\ $\equiv$ \rrx, \ 
+% \rrf\ $\equiv$ \rrz, \    \rrb\ $\equiv$ \rrzp,
+%
+% {\noindent}For example, \rrd\ is generated by  the command \cmd{\rrd}.
+%
+% {\noindent}Note that these moves do not have prime $^\prime$ versions  
+% since \rru\ is the opposite of \rrd, \rrl\ is the opposite of \rrr, and
+% \rrf\ is the opposite of \rrb.
+%
+% \DescribeMacro{\rrh..}
+% \DescribeMacro{\Rubik..}
+% As with the \rrhx, \rrhy, \rrhz\ forms (described above) there also 
+% equivalent \cmd{\rrh..} and \cmd{\Rubik..} forms. For example, 
+% \rrhd\ is generated by the command \cmd{\rrhd}.
+%
+%
+%  \subsection{Examples}
+%  \label{sec:examples}
+%  \begin{quote}
+%    \rrR\  is generated by  the `rubik rotation' command \cmd{\rrR}
+%
+%    \rrFw\  is generated by  the `rubik rotation' command \cmd{\rrFw}
+%
+%    \rrL$^2$ is generated by \cmd{\rrL}\verb!$^2$!
+%
+%    \rrRp\ is generated by \cmd{\rrRp}
+%
+%    \rrFwp\  is generated by \cmd{\rrFwp}
+%
+%        \rrx\ and \rrhy\ and \Rubikzp\ are  generated by 
+%   \cmd{\rrx}  and \cmd{\rrhy} and \cmd{\Rubikzp}
+%
+%    \rrf\ and \rrhb\ are  generated by \cmd{\rrf} and \cmd{\rrhb}
+%
+%  The sequence  \rrU\rrU\rrR\rrR\ is generated by  \cmd{\rrU}\cmd{\rrU}\cmd{\rrR}\cmd{\rrR}
+%  \end{quote}
+%  
+%  \bigskip
+%         
+%  {\noindent}\RubikF\RubikR\RubikU\Rubiky\RubikRp\RubikLwp\
+%  \ \  \verb!\RubikF\RubikR\RubikU\Rubiky\RubikRp\RubikLwp!
+%  
+%  \bigskip
+%  
+%  {\noindent}The  equivalent `text' version  of the first three 
+%  rotations above (and their commands)  are as follows:
+%  
+%  \bigskip
+%  
+%  {\noindent}\textRubikF\ \textRubikR\ \textRubikU\ \ \ \  
+%       \verb!\textRubikF\ \textRubikR\ \textRubikU!
+%  
+%  \bigskip
+%  {\noindent}Writing the first sequence using  only  letter-codes or only hieroglyphs, we have:
+%  
+%  \bigskip
+%  
+%  {\noindent}\rrF\rrR\rrU\rry\rrRp \ \ \ \
+%  \verb!\rrF\rrR\rrU\rry\rrRp!
+%  
+%  \bigskip
+%  
+%  {\noindent}\rrhF\rrhR\rrhU\rrhy\rrhRp \ \ \ \
+%  \verb!\rrhF\rrhR\rrhU\rrhy\rrhRp\! 
+%
+%  \bigskip
+% 
+% The following shows the importance of using commas to avoid ambiguity:
+%
+% \bigskip
+%
+% {\noindent}\rrD,\rrU2,\rrF2,\rrDs2,\rrB,  \ \ \ \  \verb!\rrD,\rrU2,\rrF2,\rrDs2,\rrB,!
+%
+%  \bigskip
+%
+% {\noindent}\rrhD,\rrhU2,\rrhF2,\rrhDs2,\rrhB, \ \ \ \  \verb!\rrhD,\rrhU2,\rrhF2,\rrhDs2,\rrhB,!
+% 
+%
+%  \subsection{Listing of all rotation commands}
+%   \label{sec:listofcommands}
+%
+% Note that all these commands also have a \cmd{\Rubik..} equivalent form which 
+% typesets both the hieroglyph and its lettercode in a vertical format, 
+% as shown in the above `Examples' section. These have been ommitted  here
+% owing to the difficulty of including this form easily in the following table.
+%
+% Note also that some \cmd{\rrh..} commands (eg~the \cmd{\rrhB..} commands)  
+% show only the lettercode in a square box. This is because these  rotations, which 
+%  do not have a `true' visual representation as seen from the \textsc{front} face,
+% are somewhat ambiguous unless typeset with the associated lettercode (ie using the 
+% \cmd{\Rtbik..}  or \cmd{\textRubik..} commands). 
+%
+%  \newcommand{\dnstrut}{\rule{0pt}{17pt}}
+%  \newcommand{\dns}{\hspace{2mm}}
+%  \newcommand{\dnsp}{\hspace{2mm}} 
+%
+%
+%
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4cm}}
+%  \dnstrut\rrU\dns\cmd{\rrU}
+%  & \rrhU\dns\cmd{\rrhU}
+%  & \textRubikU\dns\cmd{\textRubikU} \nonumber\\ 
+%  \dnstrut\rrUp\dns\cmd{\rrUp}
+%  & \rrhUp\dns\cmd{\rrhUp}
+%  & \textRubikUp\dns\cmd{\textRubikUp} \nonumber\\ 
+%  \dnstrut\rrUw\dns\cmd{\rrUw}
+%  & \rrhUw\dns\cmd{\rrhUw}
+%  & \textRubikUw\dns\cmd{\textRubikUw} \nonumber\\ 
+%  \dnstrut\rrUwp\dns\cmd{\rrUwp}
+%  & \rrhUwp\dns\cmd{\rrhUwp}
+%  & \textRubikUwp\dns\cmd{\textRubikUwp} \nonumber\\ 
+%  \dnstrut\rrUs\dns\cmd{\rrUs}
+%  & \rrhUs\dns\cmd{\rrhUs}
+%  & \textRubikUs\dns\cmd{\textRubikUs} \nonumber\\ 
+%  \dnstrut\rrUsp\dns\cmd{\rrUsp}
+%  & \rrhUsp\dns\cmd{\rrhUsp}
+%  & \textRubikUsp\dns\cmd{\textRubikUsp} \nonumber\\ 
+%  \dnstrut\rrUa\dns\cmd{\rrUa}
+%  & \rrhUa\dns\cmd{\rrhUa}
+%  & \textRubikUa\dns\cmd{\textRubikUa} \nonumber\\ 
+%  \dnstrut\rrUap\dns\cmd{\rrUap}
+%  & \rrhUap\dns\cmd{\rrhUap}
+%  & \textRubikUap\dns\cmd{\textRubikUap} \nonumber\\
+%  \end{supertabular}
+%
+%
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4cm}}
+%  \dnstrut\rrD\dns\cmd{\rrD}
+%  & \rrhD\dns\cmd{\rrhD}
+%  & \textRubikD\dns\cmd{\textRubikD} \nonumber\\ 
+%  \dnstrut\rrDp\dns\cmd{\rrDp}
+%  & \rrhDp\dns\cmd{\rrhDp}
+%  & \textRubikDp\dns\cmd{\textRubikDp} \nonumber\\ 
+%  \dnstrut\rrDw\dns\cmd{\rrDw}
+%  & \rrhDw\dns\cmd{\rrhDw}
+%  & \textRubikDw\dns\cmd{\textRubikDw} \nonumber\\ 
+%  \dnstrut\rrDwp\dns\cmd{\rrDwp}
+%  & \rrhDwp\dns\cmd{\rrhDwp}
+%  & \textRubikDwp\dns\cmd{\textRubikDwp} \nonumber\\ 
+%  \dnstrut\rrDs\dns\cmd{\rrDs}
+%  & \rrhDs\dns\cmd{\rrhDs}
+%  & \textRubikDs\dns\cmd{\textRubikDs} \nonumber\\ 
+%  \dnstrut\rrDsp\dns\cmd{\rrDsp}
+%  & \rrhDsp\dns\cmd{\rrhDsp}
+%  & \textRubikDsp\dns\cmd{\textRubikDsp} \nonumber\\ 
+%  \dnstrut\rrDa\dns\cmd{\rrDa}
+%  & \rrhDa\dns\cmd{\rrhDa}
+%  & \textRubikDa\dns\cmd{\textRubikDa} \nonumber\\ 
+%  \dnstrut\rrDap\dns\cmd{\rrDap}
+%  & \rrhDap\dns\cmd{\rrhDap}
+%  & \textRubikDap\dns\cmd{\textRubikDap} \nonumber\\
+%  \end{supertabular}
+%
+%
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4cm}}
+%  \dnstrut\rrL\dns\cmd{\rrL}
+%  & \rrhL\dns\cmd{\rrhL}
+%  & \textRubikL\dns\cmd{\textRubikL} \nonumber\\ 
+%  \dnstrut\rrLp\dns\cmd{\rrLp}
+%  & \rrhLp\dns\cmd{\rrhLp}
+%  & \textRubikLp\dns\cmd{\textRubikLp} \nonumber\\ 
+%  \dnstrut\rrLw\dns\cmd{\rrLw}
+%  & \rrhLw\dns\cmd{\rrhLw}
+%  & \textRubikLw\dns\cmd{\textRubikLw} \nonumber\\ 
+%  \dnstrut\rrLwp\dns\cmd{\rrLwp}
+%  & \rrhLwp\dns\cmd{\rrhLwp}
+%  & \textRubikLwp\dns\cmd{\textRubikLwp} \nonumber\\ 
+%  \dnstrut\rrLs\dns\cmd{\rrLs}
+%  & \rrhLs\dns\cmd{\rrhLs}
+%  & \textRubikLs\dns\cmd{\textRubikLs} \nonumber\\ 
+%  \dnstrut\rrLsp\dns\cmd{\rrLsp}
+%  & \rrhLsp\dns\cmd{\rrhLsp}
+%  & \textRubikLsp\dns\cmd{\textRubikLsp} \nonumber\\ 
+%  \dnstrut\rrLa\dns\cmd{\rrLa}
+%  & \rrhLa\dns\cmd{\rrhLa}
+%  & \textRubikLa\dns\cmd{\textRubikLa} \nonumber\\ 
+%  \dnstrut\rrLap\dns\cmd{\rrLap}
+%  & \rrhLap\dns\cmd{\rrhLap}
+%  & \textRubikLap\dns\cmd{\textRubikLap} \nonumber\\
+%  \end{supertabular}
+%
+%
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4cm}}
+%  \dnstrut\rrR\dns\cmd{\rrR}
+%  & \rrhR\dns\cmd{\rrhR}
+%  & \textRubikR\dns\cmd{\textRubikR} \nonumber\\ 
+%  \dnstrut\rrRp\dns\cmd{\rrRp}
+%  & \rrhRp\dns\cmd{\rrhRp}
+%  & \textRubikRp\dns\cmd{\textRubikRp} \nonumber\\ 
+%  \dnstrut\rrRw\dns\cmd{\rrRw}
+%  & \rrhRw\dns\cmd{\rrhRw}
+%  & \textRubikRw\dns\cmd{\textRubikRw} \nonumber\\ 
+%  \dnstrut\rrRwp\dns\cmd{\rrRwp}
+%  & \rrhRwp\dns\cmd{\rrhRwp}
+%  & \textRubikRwp\dns\cmd{\textRubikRwp} \nonumber\\ 
+%  \dnstrut\rrRs\dns\cmd{\rrRs}
+%  & \rrhRs\dns\cmd{\rrhRs}
+%  & \textRubikRs\dns\cmd{\textRubikRs} \nonumber\\ 
+%  \dnstrut\rrRsp\dns\cmd{\rrRsp}
+%  & \rrhRsp\dns\cmd{\rrhRsp}
+%  & \textRubikRsp\dns\cmd{\textRubikRsp} \nonumber\\ 
+%  \dnstrut\rrRa\dns\cmd{\rrRa}
+%  & \rrhRa\dns\cmd{\rrhRa}
+%  & \textRubikRa\dns\cmd{\textRubikRa} \nonumber\\ 
+%  \dnstrut\rrRap\dns\cmd{\rrRap}
+%  & \rrhRap\dns\cmd{\rrhRap}
+%  & \textRubikRap\dns\cmd{\textRubikRap} \nonumber\\
+%  \end{supertabular}
+%
+%
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4cm}}
+%  \dnstrut\rrF\dns\cmd{\rrF}
+%  & \rrhF\dns\cmd{\rrhF}
+%  & \textRubikF\dns\cmd{\textRubikF} \nonumber\\ 
+%  \dnstrut\rrFp\dns\cmd{\rrFp}
+%  & \rrhFp\dns\cmd{\rrhFp}
+%  & \textRubikFp\dns\cmd{\textRubikFp} \nonumber\\ 
+%  \dnstrut\rrFw\dns\cmd{\rrFw}
+%  & \rrhFw\dns\cmd{\rrhFw}
+%  & \textRubikFw\dns\cmd{\textRubikFw} \nonumber\\ 
+%  \dnstrut\rrFwp\dns\cmd{\rrFwp}
+%  & \rrhFwp\dns\cmd{\rrhFwp}
+%  & \textRubikFwp\dns\cmd{\textRubikFwp} \nonumber\\ 
+%  \dnstrut\rrFs\dns\cmd{\rrFs}
+%  & \rrhFs\dns\cmd{\rrhFs}
+%  & \textRubikFs\dns\cmd{\textRubikFs} \nonumber\\ 
+%  \dnstrut\rrFsp\dns\cmd{\rrFsp}
+%  & \rrhFsp\dns\cmd{\rrhFsp}
+%  & \textRubikFsp\dns\cmd{\textRubikFsp} \nonumber\\ 
+%  \dnstrut\rrFa\dns\cmd{\rrFa}
+%  & \rrhFa\dns\cmd{\rrhFa}
+%  & \textRubikFa\dns\cmd{\textRubikFa} \nonumber\\ 
+%  \dnstrut\rrFap\dns\cmd{\rrFap}
+%  & \rrhFap\dns\cmd{\rrhFap}
+%  & \textRubikFap\dns\cmd{\textRubikFap} \nonumber\\
+%  \end{supertabular}
+%
+%
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4cm}}
+%  \dnstrut\rrB\dns\cmd{\rrB}
+%  & \rrhB\dns\cmd{\rrhB}
+%  & \textRubikB\dns\cmd{\textRubikB} \nonumber\\ 
+%  \dnstrut\rrBp\dns\cmd{\rrBp}
+%  & \rrhBp\dns\cmd{\rrhBp}
+%  & \textRubikBp\dns\cmd{\textRubikBp} \nonumber\\ 
+%  \dnstrut\rrBw\dns\cmd{\rrBw}
+%  & \rrhBw\dns\cmd{\rrhBw}
+%  & \textRubikBw\dns\cmd{\textRubikBw} \nonumber\\ 
+%  \dnstrut\rrBwp\dns\cmd{\rrBwp}
+%  & \rrhBwp\dns\cmd{\rrhBwp}
+%  & \textRubikBwp\dns\cmd{\textRubikBwp} \nonumber\\ 
+%  \dnstrut\rrBs\dns\cmd{\rrBs}
+%  & \rrhBs\dns\cmd{\rrhBs}
+%  & \textRubikBs\dns\cmd{\textRubikBs} \nonumber\\ 
+%  \dnstrut\rrBsp\dns\cmd{\rrBsp}
+%  & \rrhBsp\dns\cmd{\rrhBsp}
+%  & \textRubikBsp\dns\cmd{\textRubikBsp} \nonumber\\ 
+%  \dnstrut\rrBa\dns\cmd{\rrBa}
+%  & \rrhBa\dns\cmd{\rrhBa}
+%  & \textRubikBa\dns\cmd{\textRubikBa} \nonumber\\ 
+%  \dnstrut\rrBap\dns\cmd{\rrBap}
+%  & \rrhBap\dns\cmd{\rrhBap}
+%  & \textRubikBap\dns\cmd{\textRubikBap} \nonumber\\
+%  \end{supertabular}
+%
+%
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4cm}}
+%  \dnstrut\rrSu\dns\cmd{\rrSu}
+%  & \rrhSu\dns\cmd{\rrhSu}
+%  & \textRubikSu\dns\cmd{\textRubikSu} \nonumber\\ 
+%  \dnstrut\rrSup\dns\cmd{\rrSup}
+%  & \rrhSup\dns\cmd{\rrhSup}
+%  & \textRubikSup\dns\cmd{\textRubikSup} \nonumber\\ 
+%  \dnstrut\rrSd\dns\cmd{\rrSd}
+%  & \rrhSd\dns\cmd{\rrhSd}
+%  & \textRubikSd\dns\cmd{\textRubikSd} \nonumber\\ 
+%  \dnstrut\rrSdp\dns\cmd{\rrSdp}
+%  & \rrhSdp\dns\cmd{\rrhSdp}
+%  & \textRubikSdp\dns\cmd{\textRubikSdp} \nonumber\\ 
+%  \dnstrut\rrSl\dns\cmd{\rrSl}
+%  & \rrhSl\dns\cmd{\rrhSl}
+%  & \textRubikSl\dns\cmd{\textRubikSl} \nonumber\\ 
+%  \dnstrut\rrSlp\dns\cmd{\rrSlp}
+%  & \rrhSlp\dns\cmd{\rrhSlp}
+%  & \textRubikSlp\dns\cmd{\textRubikSlp} \nonumber\\ 
+%  \dnstrut\rrSr\dns\cmd{\rrSr}
+%  & \rrhSr\dns\cmd{\rrhSr}
+%  & \textRubikSr\dns\cmd{\textRubikSr} \nonumber\\ 
+%  \dnstrut\rrSrp\dns\cmd{\rrSrp}
+%  & \rrhSrp\dns\cmd{\rrhSrp}
+%  & \textRubikSrp\dns\cmd{\textRubikSrp} \nonumber\\ 
+%  \dnstrut\rrSf\dns\cmd{\rrSf}
+%  & \rrhSf\dns\cmd{\rrhSf}
+%  & \textRubikSf\dns\cmd{\textRubikSf} \nonumber\\ 
+%  \dnstrut\rrSfp\dns\cmd{\rrSfp}
+%  & \rrhSfp\dns\cmd{\rrhSfp}
+%  & \textRubikSfp\dns\cmd{\textRubikSfp} \nonumber\\ 
+%  \dnstrut\rrSb\dns\cmd{\rrSb}
+%  & \rrhSb\dns\cmd{\rrhSb}
+%  & \textRubikSb\dns\cmd{\textRubikSb} \nonumber\\ 
+%  \dnstrut\rrSbp\dns\cmd{\rrSbp}
+%  & \rrhSbp\dns\cmd{\rrhSbp}
+%  & \textRubikSbp\dns\cmd{\textRubikSbp} \nonumber\\ 
+%  \end{supertabular}
+%
+%
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4cm}}
+%  \dnstrut\rrE\dns\cmd{\rrE}
+%  & \rrhE\dns\cmd{\rrhE}
+%  & \textRubikE\dns\cmd{\textRubikE} \nonumber\\ 
+%  \dnstrut\rrEp\dns\cmd{\rrEp}
+%  & \rrhEp\dns\cmd{\rrhEp}
+%  & \textRubikEp\dns\cmd{\textRubikEp} \nonumber\\ 
+%  \dnstrut\rrM\dns\cmd{\rrM}
+%  & \rrhM\dns\cmd{\rrhM}
+%  & \textRubikM\dns\cmd{\textRubikM} \nonumber\\ 
+%  \dnstrut\rrMp\dns\cmd{\rrMp}
+%  & \rrhMp\dns\cmd{\rrhMp}
+%  & \textRubikMp\dns\cmd{\textRubikMp} \nonumber\\ 
+%  \dnstrut\rrS\dns\cmd{\rrS}
+%  & \rrhS\dns\cmd{\rrhS}
+%  & \textRubikS\dns\cmd{\textRubikS} \nonumber\\ 
+%  \dnstrut\rrSp\dns\cmd{\rrSp}
+%  & \rrhSp\dns\cmd{\rrhSp}
+%  & \textRubikSp\dns\cmd{\textRubikSp} \nonumber\\ 
+%  \end{supertabular}
+%
+%
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4cm}}
+%  \dnstrut\rrx\dns\cmd{\rrx}
+%  & \rrhx\dns\cmd{\rrhx}
+%  & \Rubikx\dns\cmd{\Rubikx} \nonumber\\ 
+%  \dnstrut\rrxp\dns\cmd{\rrxp}
+%  & \rrhxp\dns\cmd{\rrhxp}
+%  & \Rubikxp\dns\cmd{\Rubikxp} \nonumber\\ 
+%  \dnstrut\rry\dns\cmd{\rry}
+%  & \rrhy\dns\cmd{\rrhy}
+%  & \Rubiky\dns\cmd{\Rubiky} \nonumber\\ 
+%  \dnstrut\rryp\dns\cmd{\rryp}
+%  & \rrhyp\dns\cmd{\rrhyp}
+%  & \Rubikyp\dns\cmd{\Rubikyp} \nonumber\\ 
+%  \dnstrut\rrz\dns\cmd{\rrz}
+%  & \rrhz\dns\cmd{\rrhz}
+%  & \Rubikz\dns\cmd{\Rubikz} \nonumber\\ 
+%  \dnstrut\rrzp\dns\cmd{\rrzp}
+%  & \rrhzp\dns\cmd{\rrhzp}
+%  & \Rubikzp\dns\cmd{\Rubikzp} \nonumber\\ 
+%  \end{supertabular}
+%
+%
+%  \begin{supertabular}[lll]{p{3cm} p{3cm} p{4cm}}
+%  \dnstrut\rru\dns\cmd{\rru}
+%  & \rrhu\dns\cmd{\rrhu}
+%  & \Rubiku\dns\cmd{\Rubiku} \nonumber\\ 
+%  \dnstrut\rrd\dns\cmd{\rrd}
+%  & \rrhd\dns\cmd{\rrhd}
+%  & \Rubikd\dns\cmd{\Rubikd} \nonumber\\ 
+%  \dnstrut\rrl\dns\cmd{\rrl}
+%  & \rrhl\dns\cmd{\rrhl}
+%  & \Rubikl\dns\cmd{\Rubikl} \nonumber\\ 
+%  \dnstrut\rrr\dns\cmd{\rrr}
+%  & \rrhr\dns\cmd{\rrhr}
+%  & \Rubikr\dns\cmd{\Rubikr} \nonumber\\ 
+%  \dnstrut\rrf\dns\cmd{\rrf}
+%  & \rrhf\dns\cmd{\rrhf}
+%  & \Rubikf\dns\cmd{\Rubikf} \nonumber\\ 
+%  \dnstrut\rrb\dns\cmd{\rrb}
+%  & \rrhb\dns\cmd{\rrhb}
+%  & \Rubikb\dns\cmd{\Rubikb} \nonumber\\ 
+%  \end{supertabular}
+%
+%
+%
+%    \section{Colours}
+%
+% The \rubikcube\ package defines 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{I thank Peter Bartal  
+% for pointing this out.}
+%
+% \medskip
+% \noindent\texttt{http://The-Rubiks-Cube.deviantart.com/journal/Using-Official-Rubik}
+% \newline\texttt{-s-Cube-Colors-268760351}
+%
+% \medskip
+% {\noindent}the official Rubik cube colours are defined as
+% \begin{quote}
+%\begin{verbatim}
+% .... 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 
+% may help you which I have listed below. Remember, these are
+% just approximate RGB equivalents to the official Rubik's Cube
+%  colors.
+% 
+% Red: 200C #C41E3A  (www.perbang.dk/rgb/c41e3a/)
+% Green: 347C #009E60 (www.perbang.dk/rgb/009e60/)
+% Blue: 293C #0051BA (www.perbang.dk/rgb/0051ba/)
+% Orange: 021C "Pantone Orange" #FF5800 (www.perbang.dk/rgb/ff5800/)
+% Yellow: 012C "Pantone Yellow" #FFD500 (www.perbang.dk/rgb/ffd500/)
+% White: N/A #FFFFFF
+%
+% Red    {HTML}{C41E3A}
+% green  {HTML}{009E60}
+% Blue   {HTML}{0051BA}
+% Yellow {HTML}{FFD500}
+% Orange {HTML}{FF5800}
+% White  {HTML}{FFFFFF}
+%\end{verbatim}
+% \end{quote}
+%  However, we have optimised these prescribed colours very slightly 
+%  for screen \& print use (for example, the yellow  was made very 
+%  slightly brighter),  and so the actual colours  as used by 
+%  the \rubikcube\ package  are as follows:
+%
+% \begin{quote}
+%\begin{verbatim}
+% \definecolor{R}{HTML}{C41E33}
+% \definecolor{G}{HTML}{00BE38}
+% \definecolor{B}{HTML}{0051BA}
+% \definecolor{Y}{HTML}{FFFF00}
+% \colorlet{O}{orange}
+% \colorlet{W}{white}
+% \colorlet{X}{black!30}%
+%\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
+% \begin{quote}
+%    \cmd{\colorlet\{R\}\{red\}}
+% \end{quote}
+% However, it is important to appreciate that  the letter codes 
+% ROYGBWX are `hardwired' into many of the macros in the \rubikcube\ package,
+%  so don't change these.
+%
+%
+%  \section{Rubik face coordinates}
+%  \label{sec:coordinates}
+%
+% 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. 
+%
+% \begin{figure}[hbt]
+% \centering
+% \ifpdf
+%   \includegraphics[height=3cm]{Rubik_doc_figB.pdf}
+% \else
+% \includegraphics[height=3cm]{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. 
+%  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}
+%
+% This is an important feature since knowing the location of the 
+% origin enables one to easily use any of the  TikZ commands
+% (eg~\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 \cmd{\minipage}}
+%
+%  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 TikZ 
+%  picture environment can be easily calculated. For example, if the TikZ 
+%  scale used is $0.5$, then the appropriate width of the required minipage 
+%  is $0.5 \times 4\mbox{cm} =  2\mbox{cm}$. 
+%
+% The default width of the semi-flat cube representation is 10cm, and that of the 
+% flat cube is 12cm.
+%
+%  \section{Commands}
+%
+% All  |rubikcube| commands assume a 3x3x3 cube by default.
+% There are three primary command categories:  \cmd{\Draw..} commands 
+% (which must be used \textit{inside} a TikZ picture environment), 
+% `parameter-allocation' commands (either inside or outside a TikZ environment), 
+% and commands which can be used in ordinary text (eg~rotation 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).
+%
+%
+%    \subsection{Draw commands}
+%
+%   \DescribeMacro{\DrawRubikCubeXY}
+%   \DescribeMacro{\DrawCubieXYxyz}
+% These  commands  draw Rubik cubes and  single cubies  in one of four 
+% orientations as denoted by the terminal XY viewing-direction code RU (RightUp), 
+% RD (RightDown), LU (LeftUp),  LD (LeftDown). For example, the command
+%  \begin{quote}
+%  \cmd{\DrawRubikCubeRU}
+%  \end{quote}
+% will draw a Rubik cube  as viewed from the RightUp direction, as 
+% shown in the following figure.
+% 
+% \bigskip
+%
+% \begin{minipage}{2.8cm}
+% \begin{tikzpicture}[scale=0.7]
+% \DrawRubikCubeRU 
+% \end{tikzpicture}
+% \end{minipage}
+%   \hspace{5mm}
+% \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+% \begin{tikzpicture}[scale=0.7]
+%    \DrawRubikCubeRU 
+% \end{tikzpicture}
+%\end{verbatim}
+% \end{minipage}
+%
+% \bigskip 
+%  
+% {\noindent}Note that in the above example all the cubies are displayed 
+% in the default grey colour, since no Face colours have been specified. 
+% 
+% Since \LaTeX\ commands have a maximum limit of only 9 parameters, 
+% it is necessary to use separate commands 
+% (`Face' and `Slice'  commands---see below) in order to accommodate 
+% all 27 visible colours of a 3D~Rubik cube.
+%
+% Since a single cubie has only three visible faces we can include 
+% colour parameters in \cmd{\DrawCubie} commands. Consequently \cmd{\DrawCubie}
+%  commands have the format 
+% \begin{quote}
+%  \cmd{\DrawCubieXY\{x\}\{y\}\{z\}}  
+% \end{quote}
+% where the  XY pair denote the viewing direction as before, and 
+% the xyz  denote the face colours associated with each of the three axes. 
+%
+% 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.
+% 
+% \bigskip
+%
+% \begin{minipage}{1.35cm}
+% \begin{tikzpicture}[scale=1]
+% \DrawCubieRU{O}{Y}{G} 
+% \end{tikzpicture}
+% \end{minipage}
+%    \hspace{1cm}
+% \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+% \begin{tikzpicture}[scale=1]
+%    \DrawCubieRU{O}{Y}{G} 
+% \end{tikzpicture}
+%\end{verbatim}
+% \end{minipage}
+% 
+% \bigskip 
+%
+%
+%
+% \begin{figure}[hbt]
+%   \centering
+% \ifpdf
+%    \includegraphics[height=4cm]{Rubik_doc_figC.pdf}
+%  \else
+% \includegraphics[height=4cm]{Rubik_doc_figC.eps}
+% \fi
+% \vspace{-5mm}\caption{\label{fig:cubiedydx}Cubie dy dx parameters} 
+% \end{figure}
+%
+%  \DescribeMacro{\Cubiedy}
+%  \DescribeMacro{\Cubiedx}
+%  Minor  cubie configuration changes  can be effected 
+% (within a TikZ picture environment)  by adjusting the dy and dx 
+% values ($> 0$; no units)  shown in Figure~\ref{fig:cubiedydx} 
+% via the two commands
+% \begin{quote}
+% \cmd{\Cubiedy\{\}} \\
+% \cmd{\Cubiedx\{\}} 
+% \end{quote}
+% as shown in the folowing example.
+%
+% \bigskip
+%
+% \begin{minipage}{1.7cm}
+% \begin{tikzpicture}[scale=1]
+% \Cubiedy{0.4}
+% \Cubiedx{0.8}
+% \DrawCubieRU{O}{Y}{G} 
+% \end{tikzpicture}
+% \end{minipage}
+% \hspace{2cm}
+% \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+% \begin{tikzpicture}[scale=1]
+%   \Cubiedy{0.4}
+%   \Cubiedx{0.8}
+%   \DrawCubieRU{O}{Y}{G} 
+% \end{tikzpicture}
+%\end{verbatim}
+% \end{minipage}
+% 
+% \bigskip
+%
+% {\noindent}Note that the  \textsc{front} of the cubie is a unit square, 
+% and the graphic origin of the cubie image is at the bottom left corner of the 
+% \textsc{front}  (see also the section on Arrows).
+% The default  values of dy and dx are 0.4. 
+%
+% \medskip
+%
+% \DescribeMacro{\textCubieRU}
+% \DescribeMacro{\textCubieRD}
+% \DescribeMacro{\textCubieLU}
+% \DescribeMacro{\textCubieLD}
+% For convenience, there are also four (smaller) `text' versions \textCubieRU{O}{Y}{G}   
+%  of the  four \cmd{\DrawCubie} commands for 
+% use in ordinary text, as follows:
+% \begin{quote}
+%  \textCubieRU{O}{Y}{G} \ \ |\textCubieRU{O}{Y}{G}|
+%
+% \medskip
+%
+% \textCubieRD{O}{Y}{G} \ \  |\textCubieRD{O}{Y}{G}|     
+%
+% \medskip
+%
+% \textCubieLU{O}{Y}{G}  \ \ |\textCubieLU{O}{Y}{G}|
+%
+% \medskip
+%
+%  \textCubieLD{O}{Y}{G}  \ \  |\textCubieLD{O}{Y}{G}|  
+% \end{quote}
+% Note that the \cmd{\textCubieXY} commands are not influenced by the 
+% \cmd{\Cubiedy}, \cmd{\Cubiedx} commands as their size is preset for text use. 
+%
+% Other \cmd{\Draw..} commands which we shall meet later are
+%  \texttt{DrawRubikLayerFace..},  \texttt{DrawRubikLayerSide..}, 
+% \texttt{DrawNCube..}, \texttt{DrawRubikFlat} and \texttt{DrawRubikCubeFlat}.
+%
+%
+% \subsubsection{\cmd{\draw} error message}
+%
+% See also section~\ref{drawerrormessage} regarding the error message associated with 
+% using a \cmd{\Draw...} command  \textit{outside}  a TikZ picture environment.
+%
+%
+%  \subsection{Face commands}
+%
+%  \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 
+% `\textsc{all}' command which allocates  the same colour to all the cubies 
+% on a 9-face, as follows (only a single colour argument is required):
+%
+% If you want a particular face to be \textsc{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 used, 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.
+%
+% \bigskip
+% 
+% \begin{minipage}{2.8cm}
+% \begin{tikzpicture}[scale=0.7]
+% \RubikFaceUpAll{X}
+% \RubikFaceRightAll{R}
+% \RubikFaceFront{W}{Y}{G}
+%                {W}{Y}{G}
+%                {W}{Y}{G}
+% \DrawRubikCubeRU
+% \end{tikzpicture}
+% \end{minipage}
+%    \hspace{5mm}
+% \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+% \begin{tikzpicture}[scale=0.7]
+%    \RubikFaceUpAll{X}
+%    \RubikFaceRightAll{R}
+%    \RubikFaceFront{W}{Y}{G}
+%                   {W}{Y}{G}
+%                   {W}{Y}{G}
+%    \DrawRubikCubeRU
+% \end{tikzpicture}
+%\end{verbatim}
+% \end{minipage}
+% 
+%
+% \subsection{RubikCubeSolved command}
+%
+%  \DescribeMacro{\RubikCubeSolved}
+% This command  sets all the face colours to that of a standard `solved' cube
+% as shown in the following semi-flat image.
+% This command is equivalent to the following set of face commands:
+%\begin{verbatim}
+%  \RubikFaceUpAll{W}%
+%  \RubikFaceDownAll{Y}%
+%  \RubikFaceLeftAll{B}%
+%  \RubikFaceRightAll{G}%
+%  \RubikFaceFrontAll{O}%
+%  \RubikFaceBackAll{R}%
+%\end{verbatim}
+%
+% \begin{tikzpicture}[scale=0.6]
+% \RubikCubeSolved
+% \DrawRubikCubeFlat
+% \end{tikzpicture}
+%
+%  Users can easily set their own alternative `solved'  face/colour configuration by `renewing' 
+% this command as follows---remember to include the trailing \%  (note that the colours 
+% ROYGBWX are currently hardwired  so don't  use a different set of uppercase letters).
+%\begin{verbatim}
+% \renewcommand{\RubikCubeSolved}{%
+%    \RubikFaceUpAll{..}%
+%    \RubikFaceDownAll{..}%
+%    \RubikFaceLeftAll{..}%
+%    \RubikFaceRightAll{..}%
+%    \RubikFaceFrontAll{..}%
+%    \RubikFaceBackAll{..}%
+% }
+%\end{verbatim} 
+%
+%
+%    \subsection{Slice commands}
+%
+%  \DescribeMacro{\RubikSliceTopX}
+%  \DescribeMacro{\RubikSliceEquatorX}
+%  \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, Equator, Bottom.
+% The six colour arguments  associated with a given slice run in sequence 
+% from left to right irrespective of the viewpoint, eg \#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) represented 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.
+%
+% \bigskip
+%
+% \begin{minipage}{2.8cm}
+% \centering
+% \begin{tikzpicture}[scale=0.7]
+% \RubikFaceDownAll{Y}
+% \RubikSliceTopL    {G}{G}{G} {R}{R}{R}
+% \RubikSliceEquatorL{R}{R}{R} {B}{B}{B}
+% \RubikSliceBottomL {O}{O}{O} {G}{G}{G}
+% \DrawRubikCubeLD
+% \end{tikzpicture}
+% \end{minipage}
+%    \hspace{5mm}
+% \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+% \begin{tikzpicture}[scale=0.7]
+%    \RubikFaceDownAll{Y}
+%    \RubikSliceTopL     {G}{G}{G} {R}{R}{R}
+%    \RubikSliceEquatorL {R}{R}{R} {B}{B}{B}
+%    \RubikSliceBottomL  {O}{O}{O} {G}{G}{G}
+%    \DrawRubikCubeLD
+% \end{tikzpicture}
+%\end{verbatim}
+% \end{minipage}
+%
+%
+%  \subsection{LayerFace \& LayerSide commands}
+%  \label{sec:layerface}
+%
+%  These commands are mainly  intended  for drawing  final layer 
+%  configurations (ie typically using the yellow face in the  \textsc{up} position)
+%  with or without the associated side faces of the cubies of the top layer.
+%
+%  \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.
+%  
+%  \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}
+%  \hspace{1cm}
+%  \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+%  \begin{tikzpicture}[scale=0.7]
+%     \DrawRubikLayerFace{X}{Y}{X}
+%                        {Y}{Y}{Y}
+%                        {X}{Y}{X}
+%  \end{tikzpicture}
+%\end{verbatim}
+%  \end{minipage}
+%
+% \medskip
+%
+% \subsubsection{\cmd{\draw} error message}
+%
+% See also section~\ref{drawerrormessage} regarding the error message associated with 
+% using a \cmd{\Draw...} command  \textit{outside}  a TikZ picture environment.
+%
+%  \medskip
+%
+%  \subsubsection{LayerSide}
+% 
+%  \DescribeMacro{\DrawLayerSideXYp}
+%  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 
+%   where the  XY pair define the location (X:[Left \verb!|! Middle \verb!|! Right]; 
+%  Y:[Top \verb!|! Equator \verb!|! Bottom]) of a particular cubie in the layer face.
+%
+%  \begin{figure}[hbt]
+%     \centering
+%  \ifpdf
+%     \includegraphics[height=3cm]{Rubik_doc_figD.pdf}
+%  \else
+%  \includegraphics[height=3cm]{Rubik_doc_figD.eps}
+%  \fi
+%  \vspace{-5mm}\caption{\label{fig:facenotation}LayerSide letter-codes } 
+%  \end{figure}
+% 
+%  Since corner cubies have two side faces, the `p' parameter 
+%  (p:[x\verb!|!y])  is required  to denote the directional `position' of 
+%  the cubie side-face relative to the cubicle XY position
+%  (x indicates adjacent along the x-axis, and  y indicates adjacent along the y-axis).
+%  Since edge cubies have only one side face,  the `p' parameter is optional 
+%  (for consistency), since it is not strictly  necessary.
+%
+%  \medskip\noindent\textbf{Commands}: \
+%  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 
+%
+%  \begin{quote}
+%\begin{verbatim}
+%  \DrawRubikLayerSideLE{G}
+%  \DrawRubikLayerSideLEx{G}
+%\end{verbatim}
+%  \end{quote}
+%  draws  a  single small vertical  green rectangle
+%  \begin{tikzpicture}[scale=0.5]
+%  \DrawRubikLayerSideLEx{G}
+%  \end{tikzpicture}
+%   just to the left of the Left Equator (LE) square of the 9-face.
+%  The following commands draw all three side bars of a given side (Top, Bottom, Left, Right)
+%  \begin{quote}
+%\begin{verbatim}
+%  \DrawRubikLayerSideT{}{}{}
+%  \DrawRubikLayerSideB{}{}{}
+%  \DrawRubikLayerSideL{}{}{}
+%  \DrawRubikLayerSideR{}{}{}
+%\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),
+%  while the L and R forms require the colour parameters to be in top-down 
+%  vertical order (eg, top, equator, 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}
+%\begin{verbatim}
+%  \DrawRubikLayerSideL{}
+%                      {}
+%                      {}
+%\end{verbatim}
+%  \end{quote}
+%  Extending this idea, the L and R forms are combined in the LR command, 
+%  which takes six colour arguments ordered in left-right pairs,
+%  \begin{quote}
+%\begin{verbatim}
+%  \DrawRubikLayerSideLR{}{} {}{} {}{}
+%\end{verbatim}
+%  \end{quote}
+%  so that they can also be written vertically as left-right pairs.
+%  Use of these commands is shown in the following two examples.
+%  
+%  \bigskip
+% 
+%  \begin{minipage}{2.5cm}
+%  \centering
+%  \begin{tikzpicture}[scale=0.7]
+%  
+%  
+%  \DrawRubikLayerFace{X}{Y}{X}
+%                     {Y}{Y}{Y}
+%                     {X}{Y}{X}
+%  
+%  \DrawRubikLayerSideLTy{B}
+%  \DrawRubikLayerSideLTx{O}
+%  \DrawRubikLayerSideLE{G}
+%  \DrawRubikLayerSideR{O}
+%                      {B}
+%                      {R}
+%  \DrawRubikLayerSideB{R}{G}{O}
+%  \node (LT) at (0.5, 2.5)  [red]{\small\textsf{LT}};
+%  \node (LE) at (0.5, 1.5)  [red]{\small\textsf{LE}};
+%  \end{tikzpicture}
+%  \end{minipage}
+%      \hspace{1cm}
+%  \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+%  \begin{tikzpicture}[scale=0.7]
+%     \DrawRubikLayerFace{X}{Y}{X}
+%                        {Y}{Y}{Y}
+%                        {X}{Y}{X}
+%     
+%     \DrawRubikLayerSideLTy{B}
+%     \DrawRubikLayerSideLTx{O}
+%     \DrawRubikLayerSideLE{G}
+%  
+%     \DrawRubikLayerSideR{O}{B}{R}
+%     \DrawRubikLayerSideB{R}{G}{O}
+%  
+%     \node (LT) at (0.5, 2.5) 
+%                [red]{\small\textsf{LT}};
+%     \node (LE) at (0.5, 1.5)  
+%                [red]{\small\textsf{LE}};
+%  \end{tikzpicture}
+%\end{verbatim}
+%  \end{minipage}
+%  
+%  \bigskip
+%  
+%  \begin{minipage}{2.5cm}
+%  \centering
+%  \begin{tikzpicture}[scale=0.7]
+%  
+%  \DrawRubikLayerFace{G}{Y}{R}
+%                     {Y}{Y}{Y}
+%                     {B}{Y}{Y}
+%  
+%  \DrawRubikLayerSideT {Y}{B}{B}
+%  \DrawRubikLayerSideLR{R}   {Y}
+%                       {R}   {O}
+%                       {Y}   {O}
+%  \DrawRubikLayerSideB {O}{G}{G}
+%  
+%  \end{tikzpicture}
+%  \end{minipage}
+%      \hspace{1cm}
+%  \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+%  \begin{tikzpicture}[scale=0.7]
+%     \DrawRubikLayerFace{G}{Y}{R}
+%                        {Y}{Y}{Y}
+%                        {B}{Y}{Y}
+%     
+%     \DrawRubikLayerSideT {Y}{B}{B}
+%     \DrawRubikLayerSideLR{R}   {Y}
+%                          {R}   {O}
+%                          {Y}   {O}
+%     \DrawRubikLayerSideB {O}{G}{G}  
+%  \end{tikzpicture}
+%\end{verbatim}
+%  \end{minipage}
+%  
+%  \bigskip
+%  
+%  The default values (size) of the  sidebars are as follows:
+%  width (0.3), length(1) and separation  from the square face (0.3). 
+%  Note that the default value of the length of a cubie side is 1. 
+%  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\{\}}
+%  \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.
+%  
+%  \bigskip
+%
+%  \begin{minipage}{2.5cm}
+%  \centering
+%  \begin{tikzpicture}[scale=0.7]
+%  
+%  
+%  \DrawRubikLayerFace{X}{Y}{X}
+%                     {Y}{Y}{Y}
+%                     {X}{Y}{X}
+%  
+%  \RubikSideBarWidth{0.7}
+%  \RubikSideBarLength{0.7}
+%  \DrawRubikLayerSideMTy{G}
+%  \end{tikzpicture}
+%  \end{minipage}
+%      \hspace{1cm}
+%  \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+%  \begin{tikzpicture}[scale=0.7]
+%     \DrawRubikLayerFace{X}{Y}{X}
+%                        {Y}{Y}{Y}
+%                        {X}{Y}{X}
+%     \RubikSideBarWidth{0.7}
+%     \RubikSideBarLength{0.7}
+%     \DrawRubikLayerSideMTy{G}
+%  \end{tikzpicture}
+%\end{verbatim}
+%  \end{minipage}
+%  
+%  \bigskip
+%  
+%  Note also that changing the  sidebar-width or sidebar-separation 
+%  values may well also change the surrounding white-space (use \cmd{\fbox} 
+%  to visualise this) and may therefore require some fine-tuning of the 
+%  minipage width setting in order to optimise  appearance. 
+% 
+%  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.
+%  
+%  \bigskip
+%  
+%  \begin{minipage}{2.5cm}
+%  \centering
+%  \begin{tikzpicture}[scale=0.7]
+%  \RubikFaceUp   {X}{W}{X}%
+%                 {W}{W}{W}%
+%                 {X}{W}{X}%
+%  
+%  \RubikFaceFront{O}{O}{X}%
+%                 {O}{O}{X}%
+%                 {X}{X}{W}%
+%  
+%  \RubikFaceRight{X}{G}{G}%
+%                 {X}{G}{G}%
+%                 {G}{X}{X}%
+%  \DrawRubikCubeRU
+%  
+%  \DrawRubikLayerSideL{O}{B}{R}
+%  \DrawRubikLayerSideB{R}{G}{O}
+%  \end{tikzpicture}
+%  \end{minipage}
+%        \hspace{1cm}
+%  \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+%  \begin{tikzpicture}[scale=0.7]
+%     \RubikFaceUp   {X}{W}{X}%
+%                    {W}{W}{W}%
+%                    {X}{W}{X}%
+%  
+%     \RubikFaceFront{O}{O}{X}%
+%                    {O}{O}{X}%
+%                    {X}{X}{W}%
+%  
+%     \RubikFaceRight{X}{G}{G}%
+%                    {X}{G}{G}%
+%                    {G}{X}{X}%
+%     \DrawRubikCubeRU
+%  
+%     \DrawRubikLayerSideL{O}{B}{R}
+%     \DrawRubikLayerSideB{R}{G}{O}
+%  \end{tikzpicture}
+%\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. 
+%  
+% 
+%  \subsection{Flat commands}
+%  \label{sec:flatcommands}
+%  
+%  \DescribeMacro{\DrawRubikFlat}
+%  \DescribeMacro{\DrawRubikCubeFlat}
+%  Flat commands are used to draw `flat' representations of the cube. 
+%  The most  standard format, which is generated by the command \cmd{\DrawRubikFlat},
+%  is  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}
+%  \begin{tikzpicture}[scale=0.4]
+%     \RubikCubeSolved
+%     \DrawRubikFlat
+%  \end{tikzpicture}
+%\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 (green here). 
+%  The letters were placed using the following TikZ code:
+%  
+%\begin{verbatim}
+%  \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}
+%  
+%  {\noindent}An interesting `semi-flat' alternative format  uses the standard 
+%  view of the cube  and  appends the three hidden sides 
+%  (see Rokicki \textit{etal.}, 2013),  which is generated by the 
+%  command \cmd{\DrawRubikCubeFlat} as follows.
+%  
+%  \bigskip
+%
+%  \begin{minipage}{5cm}
+%  \begin{tikzpicture}[scale=0.5]
+%  \RubikCubeSolved
+%  \DrawRubikCubeFlat
+%  \end{tikzpicture}
+%  \end{minipage}
+%  \begin{minipage}{5cm}
+%\begin{verbatim}
+%  \begin{tikzpicture}[scale=0.5]
+%     \RubikCubeSolved
+%     \DrawRubikCubeFlat
+%  \end{tikzpicture}
+%\end{verbatim}
+%  \end{minipage}
+%  
+% \medskip
+%
+% \subsubsection{\cmd{\draw} error message}
+%
+% See also section~\ref{drawerrormessage} regarding the error message associated with 
+% using a \cmd{\Draw...} command  \textit{outside}  a TikZ picture environment.
+%
+%  
+%  \section[NCube]{NCube (NxNxN)}
+%  \label{sec:NCube}
+% 
+%  \DescribeMacro{\DrawNCubeAll} 
+%  An `NCube' is  a solved NxNxN cube drawn from the RU direction; 
+%  (ie.~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}{0.4\textwidth}
+%  \begin{tikzpicture}[scale=0.5]
+%     \DrawNCubeAll{5}{O}{Y}{G}
+%  \end{tikzpicture}
+%  \end{minipage}
+%  \begin{minipage}{0.5\textwidth}
+%\begin{verbatim}
+%  \begin{tikzpicture}[scale=0.5]
+%     \DrawNCubeAll{5}{O}{Y}{G}
+%  \end{tikzpicture}
+%\end{verbatim}
+%  \end{minipage}
+%
+% \medskip
+%
+% \subsubsection{\cmd{\draw} error message}
+%
+% See also section~\ref{drawerrormessage} regarding the error message associated with 
+% using a \cmd{\Draw...} command  \textit{outside}  a TikZ picture environment.
+%  
+%
+%     \section{Arrows}
+%     \label{sec:arrows}
+%  
+%  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. 
+%  
+%  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}.
+%  Consequently the start and finish coordinates for any arrow or line are 
+%  easy to determine.
+%  
+%  \begin{figure}[hbt]
+%     \centering
+%  \ifpdf
+%     \includegraphics[height=3cm]{Rubik_doc_figE.pdf}
+%  \else
+%  \includegraphics[height=3cm]{Rubik_doc_figE.eps}
+%  \fi
+%  \vspace{-5mm}\caption{\label{fig:facegraph}RubikCubeFaceFront and RubikLayerFace coordinates} 
+%  \end{figure}
+%  
+%  Thus, to draw an `ultra thick' green  arrow  from the centre of cubie LB 
+%  (say point A) to the centre of cubie ME 
+%  (say point B)---see Figure~\ref{fig:facegraph}---we first determine 
+%  the coordinates of $A$ \& $B$, namely  $A (0.5, 0.5)$,  $B (1.5, 1.5)$.  
+%  Now, to draw the arrow from $A$ to $B$ we  just include  the following TikZ 
+%  command in the \texttt{tikzpicture} environment.
+%  \begin{quote}
+%\begin{verbatim}
+%  \draw[->,ultra thick,color=green] (0.5,0.5) -- (1.5, 1.5);
+%\end{verbatim}
+%  \end{quote}
+%  The following example shows the  cubie changes in the \textsc{up} face 
+%  generated by the rotation sequence \rrF\rrR\rrU\rrRp\rrUp\rrFp.
+%  The magenta arrows indicate movement \textit{with} cubie rotations, 
+%  while the black arrow indicates movement \textit{without} rotation.
+%  
+%  This example also highlights the fact that when there are several arrows, 
+%  the start and end positions often need to be offset slightly away from cubie centres.
+%  
+%  \bigskip
+%  \noindent
+%  \begin{minipage}{2.5cm}
+%  \centering
+%  \begin{tikzpicture}[scale=0.7]
+%  
+%  \DrawRubikLayerFaceAll{W}
+%  
+%  \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=magenta] (0.5,2.6) -- (2.5, 2.6);
+%  \draw[<->,thick,color=magenta] (0.5,0.3) -- (2.5, 0.3);
+%  \end{tikzpicture}
+%  \end{minipage}
+%  \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+%  \begin{tikzpicture}[scale=0.7]
+%  \DrawRubikLayerFaceAll{W}
+%  \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=magenta] (0.5,2.6) -- (2.5, 2.6);
+%  \draw[<->,thick,color=magenta] (0.5,0.3) -- (2.5, 0.3);
+%  \end{tikzpicture}
+%\end{verbatim}
+%  \end{minipage}
+%  
+%  \bigskip
+%  Since the coordinates shown in Figure~\ref{fig:facegraph} extend 
+%  outwards in all directions, they can also be used as a guide for drawing 
+%  arrows (or other structures) outside this 3x3 `face' square. This approach
+%  is shown in the following example, where we have changed the TikZ scale 
+%  to~0.4 in order to generate a small figure, and also  reduced the minipage
+%  width to minimise  surrounding white-space, in order to facilitate placing the 
+%  figure and the code side-by-side.
+%  
+%  \bigskip
+%  
+%  \noindent
+%  \begin{minipage}{1.8cm}
+%  \centering
+%  \begin{tikzpicture}[scale=0.4]
+%  
+%  \DrawRubikLayerFace{G}{Y}{R}%
+%                     {Y}{Y}{Y}%
+%                     {B}{Y}{Y}%
+%  
+%  \DrawRubikLayerSideT {Y}{B}{B}
+%  \DrawRubikLayerSideLR{R}   {Y}
+%                       {R}   {O}
+%                       {Y}   {O}
+%  \DrawRubikLayerSideB {O}{G}{G}
+%  
+%  \draw[->,ultra thick,color=green] (0.5,5) -- (0.5, 4);
+%  \end{tikzpicture}
+%  \end{minipage}
+%  \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+%  \begin{minipage}{1.8cm}
+%  \centering
+%  \begin{tikzpicture}[scale=0.4]
+%     \DrawRubikLayerFace{G}{Y}{R}
+%                        {Y}{Y}{Y}
+%                        {B}{Y}{Y}
+%     
+%     \DrawRubikLayerSideT {Y}{B}{B}
+%     \DrawRubikLayerSideLR{R}   {Y}
+%                          {R}   {O}
+%                          {Y}   {O}
+%     \DrawRubikLayerSideB {O}{G}{G}  
+%     \draw[->,ultra thick,color=green] (0.5,5) -- (0.5, 4);
+%  \end{tikzpicture}
+%  \end{minipage}
+%\end{verbatim}
+%  \end{minipage}
+%  
+%  \bigskip
+%  
+%  {\noindent}The following example shows an arrow on the Rubik cube. 
+%  The origin of coordinates is at the bottom left corner of the 
+%  \textsc{front} face (see Section~\ref{sec:coordinates}).
+%  
+%  \bigskip
+%  \noindent
+%  \begin{minipage}{2.8cm}
+%  \centering
+%  \begin{tikzpicture}[scale=0.7]
+%  
+%  \RubikFaceFront{O}{O}{O}
+%                 {O}{O}{X}
+%                 {X}{O}{X}
+%  
+%  \RubikFaceRight{G}{G}{G}
+%                 {X}{G}{G}
+%                 {X}{X}{X}
+%  
+%  \RubikFaceDown {X}{G}{X}
+%                 {X}{Y}{X}
+%                 {X}{X}{X}
+%  
+%  \DrawRubikCubeRD
+%  \draw[ultra thick,->,color=blue] 
+%            (1.5,0.5) -- (2.5, 1.5);
+%  \end{tikzpicture}
+%  \end{minipage}
+%     \hspace{1cm}
+%  \begin{minipage}{0.6\textwidth}
+%\begin{verbatim}
+%    \begin{tikzpicture}[scale=0.7]
+%  
+%    \RubikFaceFront{O}{O}{O}
+%                   {O}{O}{X}
+%                   {X}{O}{X}
+%  
+%    \RubikFaceRight{G}{G}{G}
+%                   {X}{G}{G}
+%                   {X}{X}{X}
+%  
+%    \RubikFaceDown {X}{G}{X}
+%                   {X}{Y}{X}
+%                   {X}{X}{X}
+%  
+%    \DrawRubikCubeRD
+%    \draw[ultra thick,->,color=blue] 
+%                (1.5,0.5) -- (2.5, 1.5);  
+%  \end{tikzpicture}
+%\end{verbatim}
+%  \end{minipage}
+%  
+%
+%
+% \section{Final example}
+%
+% We now present, as a final example, the code used to draw the  front page figure:
+%
+% \bigskip
+% \hfil
+% \begin{minipage}{2cm}
+% \centering
+% \begin{tikzpicture}[scale=0.4]
+% \RubikCubeSolved
+% \DrawRubikCubeRU
+% \end{tikzpicture}
+% \end{minipage}
+% \begin{minipage}{2cm}
+% \centering
+% \begin{tikzpicture}[scale=0.4]
+% \DrawRubikLayerFaceAll{W}
+% \DrawRubikLayerSideT {R}{R}{R}
+% \DrawRubikLayerSideLR{B}   {G}
+%                      {B}   {G}
+%                      {B}   {G}
+% \DrawRubikLayerSideB {O}{O}{O}
+% \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);
+% \end{tikzpicture}
+% \end{minipage}
+% \RubikF\RubikR\RubikU\RubikRp\RubikUp\RubikFp\
+% \ \ $\longrightarrow$
+% \begin{minipage}{2cm}
+% \centering
+% \begin{tikzpicture}[scale=0.4]
+% \DrawRubikLayerFace{W}{W}{B}
+%                    {W}{W}{O}
+%                    {W}{R}{B}
+% \DrawRubikLayerSideT {G}{G}{R}
+% \DrawRubikLayerSideLR{R}   {W}
+%                      {B}   {W}
+%                      {O}   {W}
+% \DrawRubikLayerSideB {G}{W}{O}
+% \end{tikzpicture}
+% \end{minipage}
+% \hfil
+%
+% \bigskip
+%
+%\begin{verbatim}
+% \hfil
+% \begin{minipage}{2cm}
+%   \centering
+%   \begin{tikzpicture}[scale=0.4]
+%     \RubikCubeSolved
+%     \DrawRubikCubeRU
+%   \end{tikzpicture}
+% \end{minipage}
+% \begin{minipage}{2cm}
+%   \centering
+%   \begin{tikzpicture}[scale=0.4]
+%     \DrawRubikLayerFaceAll{W}
+%     \DrawRubikLayerSideT {R}{R}{R}
+%     \DrawRubikLayerSideLR{B}   {G}
+%                          {B}   {G}
+%                          {B}   {G}
+%     \DrawRubikLayerSideB {O}{O}{O}
+%     \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);
+%   \end{tikzpicture}
+% \end{minipage}
+% \RubikF\RubikR\RubikU\RubikRp\RubikUp\RubikFp\
+% \ \ $\longrightarrow$
+% \begin{minipage}{2cm}
+%   \centering
+%   \begin{tikzpicture}[scale=0.4]
+%     \DrawRubikLayerFace{W}{W}{B}
+%                        {W}{W}{O}
+%                        {W}{R}{B}
+%     \DrawRubikLayerSideT {G}{G}{R}
+%     \DrawRubikLayerSideLR{R}   {W}
+%                          {B}   {W}
+%                          {O}   {W}
+%     \DrawRubikLayerSideB {G}{W}{O}
+%   \end{tikzpicture}
+% \end{minipage}
+% \hfil
+%\end{verbatim}
+%
+%
+%  \section{Known issues \& shortcomings}
+%
+% Please contact the authors regarding any errors, shortcomings and ideas etc. 
+%
+% \begin{itemize} 
+%  
+%  \item  The rotation hieroglyphs are optimised for a 10pt font, and  do 
+%    not scale  with document  font size. This may be implemented in the future, 
+%   and will require careful mapping of the  TikZ scale factor  to font point 
+%   size, or just replacing all length parameters by a multiple of \cmd{\em} or \cmd{\en} etc.
+%   At the moment it seems to work reasonably well with both 11pt and 12pt fonts.
+%
+%  \item The sidebars can only be drawn in relation to  either a Front face of a 
+%     cube, or a  LayerFace. 
+%
+%  \item The \textsc{front} face  as drawn using the  \cmd{\DrawNCubeAll} macro  does 
+%    not have its origin at the bottom left corner. Not regarded as a significant 
+%   problem since this macros is really just a cosmetic fix/tool for drawing a 
+%   neat NxNxN cube. 
+% 
+% \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 the initial 
+%  ideas of Bartal (2011), and have cited these instances in the code documentation. 
+%  
+%
+%
+%   \section{Future supporting 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
+%  using various programming languages, eg 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.
+%  We suggest, therefore, the following directory structure  for CTAN might be  appropriate.
+%  
+%  $$
+%  \textsc{rubik}  \left\{
+%    \begin{array}{l} 
+%    \mbox{rubiktools}\\
+%    \mbox{rubik2x}\\
+%    \mbox{rubik3x}\\
+%    \ldots\\
+%    \mbox{rubik11x}\\
+%    \end{array}
+%         \right.\\
+%  $$
+%
+%    \section{References}
+%  
+%  
+%  \begin{itemize}
+%  
+%  
+%  \item  Bartal P (2011)
+%  
+%  \url{http://tex.stackexchange.com/questions/34482/}
+%  
+%  \item Chen JJ (2004). Group theory and the Rubik's cube.
+%  \url{http://www.math.harvard.edu/~jjchen/docs/Group_Theory_and_the_Rubik's_Cube.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/}
+%  
+%  \item Garfath-Cox, A (1981). \textit{The cube},  (Bolden Publishing Co., 
+%       East Molesey, Surrey) pp.32.  [copy in British Library]
+%  
+%  
+%  \item Duvoid T (2010).
+%  M\'{e}thode simple pour remonter le Rubik's cube. 
+%  \newline\url{http://duvoid.fr/rubik/rubik-debutant-couleurs.pdf}
+%  \newline\url{http://duvoid.fr/rubik/sources/notation_en.eps}
+%  \newline\url{http://duvoid.fr/rubik/sources/rubik-debutant-couleurs.tex}
+%  
+%  \item Duvoid T (2011).
+%  M\'{e}thode avanc\'{e}e  pour remonter le Rubik's cube. 
+%  \newline\url{http://duvoid.fr/rubik/rubik-friddrich-couleurs.pdf}
+%  \newline\url{http://duvoid.fr/rubik/sources/rubik-friddrich-couleurs.tex}
+%  
+%  \item 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 Golomb SW (1982). Rubik's cube and quarks. \textit{American Scientist}; 
+%    \underline{70}, pp.~257--259.
+
+%  
+%  \item Gymrek M (2009). The mathematics of toys and games.
+%  \newline\url{http://wen.mit.edu/sp.268/www/rubik.pdf}
+%  
+%  \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/}
+%
+%
+% \item Jelinek website (Jelinek J). Rubik's cube solution method. \url{http://rubikscube.info/}    
+%  
+%  \item Joyner D (2008). \textit{Adventures in group theory: 
+%       Rubik's cube, Merlin's machine and other mathematical toys}.
+%  \url{http://mike.verdone.ca/media/rubiks.pdf}
+%  
+%  
+%  \item Kriz J and Siegel P (2008). Rubik's cube-inspired puzzles demonstrate math's simple groups.
+%  \textit{Scientific American}; [? July 2008] 
+%  
+%  
+%  \item Learntofish (2010). 
+%   \url{http://learntofish.wordpress.com/2010/10/08/20-moves-suffice-to-solve-the-rubiks-cube/}
+%
+%  \item Randelhofer website (Randelhofer W).  Pretty patterns. 
+%  \url{http://www.randelhofer.ch/rubik/patterns/U080.01.html}
+%
+%   \item Reid M. \ \  \url{http://www.math.ucf.edu/~reid/Rubik/}
+%
+%  
+%  \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.
+%  (\url{http://tomas.rokicki.com/rubik20.pdf})
+%
+%  \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 Tran R (2005). A mathematical approach to solving Rubik's cube.
+%  \url{http://www.math.ubc.ca/~cass/courses/m308/projects/rtran/rtran.pdf}
+%  
+%
+%  \item Treep A and  Waterman M (1987). Marc Waterman's Algorithm, Part 2. 
+%    \textit{Cubism For Fun 15}, p.~10 (Nederlandse Kubus Club)
+%    [cited from \textit{Wikipedia} (Rubik's cube)]
+
+%  
+%  \item Vandenbergh L. \ \ \textsc{cubezone} (\url{http://www.cubezone.be}).
+%  
+%  \item WCA (2012). World Cube Association Regulations. See Section~12 for notation.
+%   \url{http://www.worldcubeassociation.org/regulations.htm}
+%  
+%  
+%  \end{itemize}
+%  
+%
+%
+% ^^A ==================================================
+% \StopEventually{\PrintIndex}
+%
+%
+%
+% \section{The code} 
+%  
+%  The conventions  we adopt regarding  capital letters and the 
+%  XYZ argument ordering are detailed in  Section~\ref{sec:conventions}.
+%
+%
+%   \subsection{    Package heading}
+%
+%    \begin{macrocode}
+%<*rubikcube>
+\def\RCfileversion{2.0}%
+\def\RCfiledate{2014/01/20}%
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{rubikcube}[\RCfiledate\space (v\RCfileversion)]
+%    \end{macrocode}
+%  The package requires TikZ
+%    \begin{macrocode}
+\@ifpackageloaded{tikz}{}{%
+  \typeout{---rubikcube requires the TikZ package.}%
+  \RequirePackage{tikz}}%
+%    \end{macrocode}
+%
+%    \begin{macro}{\rubikcube}
+%  First we create a suitable logo
+%    \begin{macrocode}
+\newcommand{\rubikcube}{\textsf{rubikcube}}%
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+%   \subsection{    Some useful internal commands}
+%
+%  \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 \textsc{front} representation 
+% (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 
+% letter-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}%
+%    \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}
+%
+%
+%   \subsection{    Colours}
+%
+%  These colour allocations were initially defined by Peter Bartal (2011).
+%  Now modified so that grey is defined as {black!30}.
+%
+%    \begin{macrocode}
+\definecolor{R}{HTML}{C41E33}%
+\definecolor{G}{HTML}{00BE38}%
+\definecolor{B}{HTML}{0051BA}%
+\definecolor{Y}{HTML}{FFFF00}%
+\colorlet{X}{black!30}% grey
+\colorlet{O}{orange}%
+\colorlet{W}{white}%
+%    \end{macrocode}
+%
+%  \subsection{    Face commands}
+%
+% Cubeface notation = U,D,L,R,F,B (Singmaster)
+% {\newline}Cubiesquare notation = t,b,l,r = top,bottom,left,right.
+% Need to use t,b for cubiesquares to avoid confusion with cubeFace notation.
+% Number the cubiesquares on a face 1-9, starting topleft, ending bottom right, as follows: 
+% {\newline}\strut\hspace{1cm}Up row \ \ \ \ \ (1,2,3) = tl, tm, tr
+% {\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} 
+%  \begin{macro}{\RubikFaceDown} 
+%  \begin{macro}{\RubikFaceLeft} 
+%  \begin{macro}{\RubikFaceRight} 
+%  \begin{macro}{\RubikFaceFront}  
+%  \begin{macro}{\RubikFaceBack}  
+% These 5 commands allocate a colour to each of the 9 cubiesquares in the 
+% specified face (Up, Down, Left, Right, Front, Back).  Each command takes 9 arguments 
+% (colour codes) in the order 1--9 as specified above. 
+%
+% {\noindent}For example, \cmd{\RubikFaceUp\{R\}\{O\}\{Y\} \{G\}\{B\}\{W\} \{X\}\{R\}\{G\}}
+%
+%
+% {\noindent}Each of the 9 \cmd{\def\{\}} commands below allocates one colour 
+% to a specific cubiesquare, using a simple three-letter encoding. 
+% 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\}} 
+% the U stands for the Up face of the cube, while the \texttt{rt} stands 
+% for the ``right-top'' cubiesquare on this face. Note that the order 
+% of the two lowercase letters (in this case \texttt{rt}) are written 
+% in the $x,y$ order; ie the first of the two lowercase letters relates to the $x$ 
+% direction (either left, middle, or right), while the second  lowercase letter 
+% relates to the $y$  direction (either top, middle, or bottom)
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro} 
+%  \end{macro}
+%  \end{macro}
+%    \begin{macrocode}
+\newcommand{\RubikFaceUp}[9]{%
+\def\Ult{#1}\def\Umt{#2}\def\Urt{#3}% 
+\def\Ulm{#4}\def\Umm{#5}\def\Urm{#6}%
+\def\Ulb{#7}\def\Umb{#8}\def\Urb{#9}%
+}   
+\newcommand{\RubikFaceFront}[9]{%
+\def\Flt{#1}\def\Fmt{#2}\def\Frt{#3}% 
+\def\Flm{#4}\def\Fmm{#5}\def\Frm{#6}%
+\def\Flb{#7}\def\Fmb{#8}\def\Frb{#9}%
+}
+\newcommand{\RubikFaceRight}[9]{%
+\def\Rlt{#1}\def\Rmt{#2}\def\Rrt{#3}% 
+\def\Rlm{#4}\def\Rmm{#5}\def\Rrm{#6}%
+\def\Rlb{#7}\def\Rmb{#8}\def\Rrb{#9}%
+}
+\newcommand{\RubikFaceDown}[9]{%
+\def\Dlt{#1}\def\Dmt{#2}\def\Drt{#3}% 
+\def\Dlm{#4}\def\Dmm{#5}\def\Drm{#6}%
+\def\Dlb{#7}\def\Dmb{#8}\def\Drb{#9}%
+}
+\newcommand{\RubikFaceLeft}[9]{%
+\def\Llt{#1}\def\Lmt{#2}\def\Lrt{#3}% 
+\def\Llm{#4}\def\Lmm{#5}\def\Lrm{#6}%
+\def\Llb{#7}\def\Lmb{#8}\def\Lrb{#9}%
+}
+\newcommand{\RubikFaceBack}[9]{%
+\def\Blt{#1}\def\Bmt{#2}\def\Brt{#3}% 
+\def\Blm{#4}\def\Bmm{#5}\def\Brm{#6}%
+\def\Blb{#7}\def\Bmb{#8}\def\Brb{#9}%
+}
+%    \end{macrocode}
+%
+%  \begin{macro}{\RubikFaceUpAll} 
+%  \begin{macro}{\RubikFaceDownAll} 
+%  \begin{macro}{\RubikFaceLeftAll} 
+%  \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).
+%
+% {\noindent}For example, \cmd{\RubikFaceUpAll\{R\}}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro} 
+%  \end{macro}
+%  \end{macro}
+%    \begin{macrocode}
+\newcommand{\RubikFaceUpAll}[1]{%
+\def\Ult{#1}\def\Umt{#1}\def\Urt{#1}% 
+\def\Ulm{#1}\def\Umm{#1}\def\Urm{#1}%
+\def\Ulb{#1}\def\Umb{#1}\def\Urb{#1}%
+}
+\newcommand{\RubikFaceFrontAll}[1]{%
+\def\Flt{#1}\def\Fmt{#1}\def\Frt{#1}% 
+\def\Flm{#1}\def\Fmm{#1}\def\Frm{#1}%
+\def\Flb{#1}\def\Fmb{#1}\def\Frb{#1}%
+}
+\newcommand{\RubikFaceRightAll}[1]{%
+\def\Rlt{#1}\def\Rmt{#1}\def\Rrt{#1}% 
+\def\Rlm{#1}\def\Rmm{#1}\def\Rrm{#1}%
+\def\Rlb{#1}\def\Rmb{#1}\def\Rrb{#1}%
+}
+\newcommand{\RubikFaceLeftAll}[1]{%
+\def\Llt{#1}\def\Lmt{#1}\def\Lrt{#1}% 
+\def\Llm{#1}\def\Lmm{#1}\def\Lrm{#1}%
+\def\Llb{#1}\def\Lmb{#1}\def\Lrb{#1}%
+}
+\newcommand{\RubikFaceDownAll}[1]{%
+\def\Dlt{#1}\def\Dmt{#1}\def\Drt{#1}% 
+\def\Dlm{#1}\def\Dmm{#1}\def\Drm{#1}%
+\def\Dlb{#1}\def\Dmb{#1}\def\Drb{#1}%
+}
+\newcommand{\RubikFaceBackAll}[1]{%
+\def\Blt{#1}\def\Bmt{#1}\def\Brt{#1}% 
+\def\Blm{#1}\def\Bmm{#1}\def\Brm{#1}%
+\def\Blb{#1}\def\Bmb{#1}\def\Brb{#1}%
+}
+%    \end{macrocode}
+%
+% {\noindent}We now use these commands to initialise all visible faces to  default colour grey (X)
+%
+% \begin{macrocode}
+\RubikFaceUpAll{X}%
+\RubikFaceDownAll{X}%
+\RubikFaceLeftAll{X}%
+\RubikFaceRightAll{X}%
+\RubikFaceFrontAll{X}%
+\RubikFaceBackAll{X}%
+%    \end{macrocode}
+%
+%
+%   \subsection{  RubikCubeSolved command}
+%
+%    \begin{macro}{\RubikCubeSolved}
+% This command sets the face/colour configuration (state) of a  typical 
+% solved Rubik cube. 
+%    \begin{macrocode}
+\newcommand{\RubikCubeSolved}{%
+  \RubikFaceUpAll{W}%
+  \RubikFaceDownAll{Y}%
+  \RubikFaceLeftAll{B}%
+  \RubikFaceRightAll{G}%
+  \RubikFaceFrontAll{O}%
+  \RubikFaceBackAll{R}%
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+% \subsection{    Slice macros}
+%
+% \begin{macro}{\RubikSliceTopR} 
+% \begin{macro}{\RubikSliceTopL} 
+% \begin{macro}{\RubikSliceEquatorR} 
+% \begin{macro}{\RubikSliceEquatorL} 
+% \begin{macro}{\RubikSliceBottomR} 
+% \begin{macro}{\RubikSliceBottomL} 
+% These 6 commands allocate colours for the 6 visible ordered 
+% cubiesquares along the side  of  a horizontal slice  
+% ordered 1--6 from left to right. We require  both  L view  
+% and R view versions.
+%    \begin{macrocode}
+\newcommand{\RubikSliceTopR}[6]{% 
+\def\Flt{#1}\def\Fmt{#2}\def\Frt{#3}% 
+\def\Rlt{#4}\def\Rmt{#5}\def\Rrt{#6}%
+} 
+\newcommand{\RubikSliceTopL}[6]{% 
+\def\Llt{#1}\def\Lmt{#2}\def\Lrt{#3}% 
+\def\Flt{#4}\def\Fmt{#5}\def\Frt{#6}%
+} 
+\newcommand{\RubikSliceEquatorR}[6]{% 
+\def\Flm{#1}\def\Fmm{#2}\def\Frm{#3}%
+\def\Rlm{#4}\def\Rmm{#5}\def\Rrm{#6}%
+} 
+\newcommand{\RubikSliceEquatorL}[6]{% 
+\def\Llm{#1}\def\Lmm{#2}\def\Lrm{#3}%
+\def\Flm{#4}\def\Fmm{#5}\def\Frm{#6}%
+} 
+\newcommand{\RubikSliceBottomR}[6]{% 
+\def\Flb{#1}\def\Fmb{#2}\def\Frb{#3}%
+\def\Rlb{#4}\def\Rmb{#5}\def\Rrb{#6}%
+} 
+\newcommand{\RubikSliceBottomL}[6]{% 
+\def\Llb{#1}\def\Lmb{#2}\def\Lrb{#3}%
+\def\Flb{#4}\def\Fmb{#5}\def\Frb{#6}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+%      \subsection{    Cube drawing macros}
+%
+% Since the three visible sides of a Rubik cube have up to  27  non-grey colours, 
+% 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). 
+% The order of the XY code is important: X first, Y second.
+%
+% On each face the cubies are drawn in the following order: Top row 
+% (left to right), Middle row (left to right), Bottom row (left to right).
+%
+% The TikZ  draw cycle for each cubie square on a Rubik cube face cycles 
+% through the  four corners of the cubie 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) origin at bottom left of front face.
+%
+%  \begin{macro}{\DrawRubikCubeFrontFace}
+% This `FrontFace' command  is an `internal' command  which draws and paints 
+% all the cubiesquares on the front face of a cube.  It is used by all 
+% of the  cube drawing macros which display the front face. 
+% The 9 colours are allocated by an earlier \cmd{\RubikFaceFront} command.
+% These Face macros are based, in part, on those of Peter Bartal (2011).
+%    \begin{macrocode}
+\newcommand{\DrawRubikCubeFrontFace}{%
+%  ---top row left to right
+\draw[line join=round,line cap=round,ultra thick,fill=\Flt]%
+(0,2) -- (0, 3) -- (1,3) -- (1,2)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Fmt]%
+(1,2) -- (1, 3) -- (2,3) -- (2,2) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Frt]%
+(2,2) -- (2, 3) -- (3,3) -- (3,2) -- cycle;
+% -----middle row left to right
+\draw[line join=round,line cap=round,ultra thick,fill=\Flm]%
+(0,1) -- (0, 2) -- (1,2) -- (1,1)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Fmm]%
+(1,1) -- (1, 2) -- (2,2) -- (2,1) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Frm]%
+(2,1) -- (2, 2) -- (3,2) -- (3,1) -- cycle;
+% ----bottom row left to right
+\draw[line join=round,line cap=round,ultra thick,fill=\Flb]%
+(0,0) -- (0, 1) -- (1,1) -- (1,0)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Fmb]%
+(1,0) -- (1, 1) -- (2,1) -- (2,0) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Frb]%
+(2,0) -- (2, 1) -- (3,1) -- (3,0) -- cycle;
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%      \subsubsection{    Viewing direction}
+%
+%  The command  `DrawRubikCubeXY' command uses a trailing XY code
+%  to specify  the  view direction (X = either R, L; Y = either U, D). 
+%  The order of the XY code is important: X first, Y second (so its easy
+%  to remember).
+%
+%  \begin{macro}{\DrawRubikCubeRU}
+% This command draws and paints a Rubik cube  as viewed from 
+% the Right Upper (RU) viewpoint. It starts by using the internal 
+% command \cmd{\DrawRubikCubeFrontFace} to draw the Front face, 
+% and then draws the Up face  followed by the Right face.
+% The colours are allocated by  the last \cmd{\RubikFaceUp}
+% and \cmd{\RubikFaceRight}  commands. 
+%    \end{macro}
+%    \begin{macrocode}
+\newcommand{\DrawRubikCubeRU}{%
+\DrawRubikCubeFrontFace %% frontface
+%%-----------Up face----------
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Ult]%
+(0.66,3.66) -- (1,4) -- (2,4) -- (1.66,3.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Umt]%
+(1.66,3.66) -- (2,4) -- (3,4) -- (2.66,3.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Urt]%
+(2.66,3.66) -- (3,4) -- (4,4) -- (3.66,3.66)  -- cycle;
+%%---middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Ulm]%
+(0.33,3.33) -- (0.66,3.66) -- (1.66,3.66) -- (1.33,3.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Umm]%
+(1.33,3.33) -- (1.66,3.66) -- (2.66,3.66) -- (2.33,3.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Urm]%
+(2.33,3.33) -- (2.66,3.66) -- (3.66,3.66) -- (3.33,3.33)  -- cycle;
+%%---bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Ulb]%
+(0,3) -- (0.33,3.33) -- (1.33,3.33) -- (1,3)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Umb]%
+(1,3) -- (1.33,3.33) -- (2.33,3.33) -- (2,3)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Urb]%
+(2,3) -- (2.33,3.33) -- (3.33,3.33) -- (3,3)  -- cycle;
+%%-----------Right face----------
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Rlt]%
+(3,2) -- (3, 3) -- (3.33,3.33) -- (3.33,2.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rmt]%
+(3.33,2.33) -- (3.33, 3.33) -- (3.66,3.66) -- (3.66,2.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rrt]%
+(3.66,2.66) -- (3.66, 3.66) -- (4,4) -- (4,3)  -- cycle;
+%%---middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Rlm]%
+(3,1) -- (3, 2) -- (3.33,2.33) -- (3.33,1.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rmm]%
+(3.33,1.33) -- (3.33, 2.33) -- (3.66,2.66) -- (3.66,1.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rrm]%
+(3.66,1.66) -- (3.66, 2.66) -- (4,3) -- (4,2)  -- cycle;
+%%---bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Rlb]%
+(3,0) -- (3, 1) -- (3.33,1.33) -- (3.33,0.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rmb]%
+(3.33,0.33) -- (3.33, 1.33) -- (3.66,1.66) -- (3.66,0.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rrb]%
+(3.66,0.66) -- (3.66, 1.66) -- (4,2) -- (4,1)  -- cycle;
+}
+%    \end{macrocode}
+%
+% \begin{macro}{\DrawRubikCube}
+% This command  is equivalent to the previous \cmd{\DrawRubikCubeRU}
+% and hence is the default form (ie if one omits the trailing XY 
+% viewpoint code).
+% \end{macro}
+%    \begin{macrocode}
+\newcommand{\DrawRubikCube}{\DrawRubikCubeRU}
+%    \end{macrocode}
+%
+%
+% \begin{macro}{\DrawRubikCubeRD}
+% This command draws and paints a Rubik cube  as viewed from 
+% the Right Down (RD) viewpoint.
+% \end{macro}
+%    \begin{macrocode}
+\newcommand{\DrawRubikCubeRD}{%
+\DrawRubikCubeFrontFace %% frontface
+%%----------Right face--------
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Rlt]%
+(3,2) -- (3, 3) -- (3.33,2.66) -- (3.33,1.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rmt]%
+(3.33,1.66) -- (3.33, 2.66) -- (3.66,2.33) -- (3.66,1.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rrt]%
+(3.66,1.33) -- (3.66, 2.33) -- (4,2) -- (4,1)  -- cycle;
+%%---middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Rlm]%
+(3,1) -- (3, 2) -- (3.33,1.66) -- (3.33,0.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rmm]%
+(3.33,0.66) -- (3.33, 1.66) -- (3.66,1.33) -- (3.66,0.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rrm]%
+(3.66,0.33) -- (3.66, 1.33) -- (4,1) -- (4,0)  -- cycle;
+%%---bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Rlb]%
+(3,0) -- (3, 1) -- (3.33,0.66) -- (3.33,-0.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rmb]%
+(3.33,-0.33) -- (3.33, 0.66) -- (3.66,0.33) -- (3.66,-0.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rrb]%
+(3.66,-0.66) -- (3.66, 0.33) -- (4,0) -- (4,-1)  -- cycle;
+%%-----------Down face---------
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Dlt]%
+(0.33,-0.33) -- (0, 0) -- (1,0) -- (1.33,-0.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Dmt]%
+(1.33,-0.33) -- (1, 0) -- (2,0) -- (2.33,-0.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Drt]%
+(2.33,-0.33) -- (2, 0) -- (3,0) -- (3.33,-0.33)  -- cycle;
+%%---middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Dlm]%
+(0.66,-0.66) -- (0.33, -0.33) -- (1.33,-0.33) -- (1.66,-0.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Dmm]%
+(1.66,-0.66) -- (1.33, -0.33) -- (2.33,-0.33) -- (2.66,-0.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Drm]%
+(2.66,-0.66) -- (2.33, -0.33) -- (3.33,-0.33) -- (3.66,-0.66)  -- cycle;
+%%---bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Dlb]%
+(1,-1) -- (0.66, -0.66) -- (1.66,-0.66) -- (2,-1)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Dmb]%
+(2,-1) -- (1.66, -0.66) -- (2.66,-0.66) -- (3,-1)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Drb]%
+(3,-1) -- (2.66, -0.66) -- (3.66,-0.66) -- (4,-1)  -- cycle;
+}
+%    \end{macrocode}
+%
+% \begin{macro}{\DrawRubikCubeLD}
+% This command draws and paints a Rubik cube  as viewed from 
+% the Left Down (LD) viewpoint.
+% \end{macro}
+%    \begin{macrocode}
+\newcommand{\DrawRubikCubeLD}{%
+\DrawRubikCubeFrontFace %% frontface
+%%------------Left face--------
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Llt]%
+(-1,1) -- (-1, 2) -- (-0.66,2.33) -- (-0.66,1.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lmt]%
+(-0.66,1.33) -- (-0.66, 2.33) -- (-0.33,2.66) -- (-0.33,1.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lrt]%
+(-0.33,1.66) -- (-0.33, 2.66) -- (0,3) -- (0,2)  -- cycle;
+%%---middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Llm]%
+(-1,0) -- (-1, 1) -- (-0.66,1.33) -- (-0.66,0.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lmm]%
+(-0.66,0.33) -- (-0.66, 1.33) -- (-0.33,1.66) -- (-0.33,0.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lrm]%
+(-0.33,0.66) -- (-0.33, 1.66) -- (0,2) -- (0,1)  -- cycle;
+%%---bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Llb]%
+(-1,-1) -- (-1, 0) -- (-0.66,0.33) -- (-0.66,-0.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lmb]%
+(-0.66,-0.66) -- (-0.66, 0.33) -- (-0.33,0.66) -- (-0.33,-0.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lrb]%
+(-0.33,-0.33) -- (-0.33, 0.66) -- (0,1) -- (0,0)  -- cycle;
+%%------------Down face----------
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Dlt]%
+(-0.33,-0.33) -- (0, 0) -- (1,0) -- (0.66,-0.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Dmt]%
+(0.66,-0.33) -- (1, 0) -- (2,0) -- (1.66,-0.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Drt]%
+(1.66,-0.33) -- (2, 0) -- (3,0) -- (2.66,-0.33)  -- cycle;
+%%---middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Dlm]%
+(-0.66,-0.66) -- (-0.33, -0.33) -- (0.66,-0.33) -- (0.33,-0.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Dmm]%
+(0.33,-0.66) -- (0.66, -0.33) -- (1.66,-0.33) -- (1.33,-0.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Drm]%
+(1.33,-0.66) -- (1.66, -0.33) -- (2.66,-0.33) -- (2.33,-0.66)  -- cycle;
+%%---bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Dlb]%
+(-1,-1) -- (-0.66, -0.66) -- (0.33,-0.66) -- (0,-1)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Dmb]%
+(0,-1) -- (0.33, -0.66) -- (1.33,-0.66) -- (1,-1)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Drb]%
+(1,-1) -- (1.33, -0.66) -- (2.33,-0.66) -- (2,-1)  -- cycle;
+}
+%    \end{macrocode}
+%
+%
+% \begin{macro}{\DrawRubikCubeLU}
+% This command draws and paints a Rubik cube  as viewed from 
+% the Left Up (LU) viewpoint.
+% \end{macro}
+%    \begin{macrocode}
+\newcommand{\DrawRubikCubeLU}{%
+\DrawRubikCubeFrontFace %% frontface
+%%-----------Left face-----------
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Llt]%
+(-1,3) -- (-1, 4) -- (-0.66,3.66) -- (-0.66,2.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lmt]%
+(-0.66,2.66) -- (-0.66, 3.66) -- (-0.33,3.33) -- (-0.33,2.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lrt]%
+(-0.33,2.33) -- (-0.33, 3.33) -- (0,3) -- (0,2)  -- cycle;
+%%---middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Llm]%
+(-1,2) -- (-1, 3) -- (-0.66,2.66) -- (-0.66,1.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lmm]%
+(-0.66,1.66) -- (-0.66, 2.66) -- (-0.33,2.33) -- (-0.33,1.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lrm]%
+(-0.33,1.33) -- (-0.33, 2.33) -- (0,2) -- (0,1)  -- cycle;
+%%---bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Llb]%
+(-1,1) -- (-1, 2) -- (-0.66,1.66) -- (-0.66,0.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lmb]%
+(-0.66,0.66) -- (-0.66, 1.66) -- (-0.33,1.33) -- (-0.33,0.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lrb]%
+(-0.33,0.33) -- (-0.33, 1.33) -- (0,1) -- (0,0)  -- cycle;
+%%-----------Up face---------
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Ult]%
+(-0.66,3.66) -- (-1, 4) -- (0,4) -- (0.33,3.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Umt]%
+(0.33,3.66) -- (0, 4) -- (1,4) -- (1.33,3.66)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Urt]%
+(1.33,3.66) -- (1, 4) -- (2,4) -- (2.33,3.66)  -- cycle;
+%%---middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Ulm]%
+(-0.33,3.33) -- (-0.66, 3.66) -- (0.33,3.66) -- (0.66,3.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Umm]%
+(0.66,3.33) -- (0.33, 3.66) -- (1.33,3.66) -- (1.66,3.33)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Urm]%
+(1.66,3.33) -- (1.33, 3.66) -- (2.33,3.66) -- (2.66,3.33)  -- cycle;
+%%---bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Ulb]%
+(0,3) -- (-0.33, 3.33) -- (0.66,3.33) -- (1,3)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Umb]%
+(1,3) -- (0.66, 3.33) -- (1.66,3.33) -- (2,3)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Urb]%
+(2,3) -- (1.66, 3.33) -- (2.66,3.33) -- (3,3)  -- cycle;%
+\ %%trailing space 
+}
+%    \end{macrocode}
+%
+%
+%   \subsection{    LayerFace commands}
+%
+%  \begin{macro}{\DrawRubikLayerFace}
+%  \begin{macro}{\DrawRubikLayerFaceAll}
+%  [Nov 2, 2013] These two LayerFace commands draw and paint a single  
+%  9-cubie face. 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 cubie etc.)
+%  The second takes only one colour parameter (since all the 
+%  colours are the same).
+%  The drawing origin (0,0) = bottom left corner. Cubies are drawn
+%  from left to right.
+%  NOTE: this macro is SAME as the  internal command 
+%  \cmd{\DrawRubikCubeFrontFace}
+%    which is used for drawing the front face of a  cube.
+% \end{macro}
+% \end{macro}
+%    \begin{macrocode}
+\newcommand{\DrawRubikLayerFace}[9]{%
+%%-----------FRONT face---------
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+(0,2) -- (0, 3) -- (1,3) -- (1,2)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=#2]%
+(1,2) -- (1, 3) -- (2,3) -- (2,2) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=#3]%
+(2,2) -- (2, 3) -- (3,3) -- (3,2) -- cycle;
+%%-----middle row
+\draw[line join=round,line cap=round,ultra thick,fill=#4]%
+(0,1) -- (0, 2) -- (1,2) -- (1,1)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=#5]%
+(1,1) -- (1, 2) -- (2,2) -- (2,1) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=#6]%
+(2,1) -- (2, 2) -- (3,2) -- (3,1) -- cycle;
+%%----bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=#7]%
+(0,0) -- (0, 1) -- (1,1) -- (1,0)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=#8]%
+(1,0) -- (1, 1) -- (2,1) -- (2,0) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=#9]%
+(2,0) -- (2, 1) -- (3,1) -- (3,0) -- cycle;
+}
+\newcommand{\DrawRubikLayerFaceAll}[1]{%
+%%----------FRONT face-----------
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+(0,2) -- (0, 3) -- (1,3) -- (1,2)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+(1,2) -- (1, 3) -- (2,3) -- (2,2) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+(2,2) -- (2, 3) -- (3,3) -- (3,2) -- cycle;
+%%-----middle row
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+(0,1) -- (0, 2) -- (1,2) -- (1,1)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+(1,1) -- (1, 2) -- (2,2) -- (2,1) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+(2,1) -- (2, 2) -- (3,2) -- (3,1) -- cycle;
+%%----bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+(0,0) -- (0, 1) -- (1,1) -- (1,0)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+(1,0) -- (1, 1) -- (2,1) -- (2,0) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+(2,0) -- (2, 1) -- (3,1) -- (3,0) -- cycle;
+}
+%    \end{macrocode}
+%
+%
+%   \subsection{    Flat commands}
+%
+%  \begin{macro}{\FlatUp}
+%  \begin{macro}{\FlatDown}
+%  \begin{macro}{\FlatLeft}
+%  \begin{macro}{\FlatRight}
+%  \begin{macro}{\FlatFront}
+%  \begin{macro}{\FlatBack}
+%  Each of these six internal `Flat'  commands draws a separate face.
+%  Each command (except \cmd{\FlatFront}) takes two arguments, 
+%  namely an  X-coordinate  and Y-coordinate of the bottom left 
+%  corner of the  face.  This (X,Y) pair allows the user to position
+%  the face. Note that the \cmd{\FlatFront} command takes no arguments,
+%  since by definition the bottom left corner of this face is (0,0).
+%
+%  \textsc{example}: The following command positions the Up face so 
+%  that its bottom left corner is located at (0,3): 
+%  \begin{quote}
+%    \cmd{\FlatUp\{0\}\{3\}}
+%  \end{quote}
+%  These internal commands are used  by the commands \cmd{\DrawRubikFlat}  
+%  and \cmd{\DrawRubikCubeFlat} to draw various flat representations 
+%  of a Rubik's cube.
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%    \begin{macrocode}
+\newcommand{\FlatUp}[2]{%
+\pgfmathsetmacro{\ux}{#1}%
+\pgfmathsetmacro{\uy}{#2}%
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Ult]%
+(\ux + 0,\uy + 2) -- (\ux + 0,\uy + 3) -- (\ux + 1,\uy + 3)%
+ -- (\ux + 1,\uy + 2)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Umt]%
+(\ux + 1,\uy + 2) -- (\ux + 1,\uy + 3) -- (\ux + 2,\uy + 3)%
+ -- (\ux + 2,\uy + 2) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Urt]%
+(\ux + 2,\uy + 2) -- (\ux + 2,\uy + 3) -- (\ux + 3,\uy + 3)%
+ -- (\ux + 3,\uy + 2) -- cycle;
+%%-----middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Ulm]%
+(\ux + 0,\uy + 1) -- (\ux + 0,\uy + 2) -- (\ux + 1,\uy + 2)%
+ -- (\ux + 1,\uy + 1)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Umm]%
+(\ux + 1,\uy + 1) -- (\ux + 1,\uy + 2) -- (\ux + 2,\uy + 2)%
+ -- (\ux + 2,\uy + 1) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Urm]%
+(\ux + 2,\uy + 1) -- (\ux + 2,\uy + 2) -- (\ux + 3,\uy + 2)%
+ -- (\ux + 3,\uy + 1) -- cycle;
+%%----bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Ulb]%
+(\ux + 0,\uy + 0) -- (\ux + 0,\uy + 1) -- (\ux + 1,\uy + 1)%
+ -- (\ux + 1,\uy + 0)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Umb]%
+(\ux + 1,\uy + 0) -- (\ux + 1,\uy + 1) -- (\ux + 2,\uy + 1)%
+ -- (\ux + 2,\uy + 0) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Urb]%
+(\ux + 2,\uy + 0) -- (\ux + 2,\uy + 1) -- (\ux + 3,\uy + 1)%
+ -- (\ux + 3,\uy + 0) -- cycle;
+}
+%%-------------------------
+\newcommand{\FlatDown}[2]{%
+\pgfmathsetmacro{\ddx}{#1}%
+\pgfmathsetmacro{\ddy}{#2}%
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Dlt]%
+(\ddx + 0,\ddy + 2) -- (\ddx + 0,\ddy + 3) -- (\ddx + 1,\ddy + 3)%
+ -- (\ddx + 1,\ddy + 2)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Dmt]%
+(\ddx + 1,\ddy + 2) -- (\ddx + 1,\ddy + 3) -- (\ddx + 2,\ddy + 3)%
+ -- (\ddx + 2,\ddy + 2) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Drt]%
+(\ddx + 2,\ddy + 2) -- (\ddx + 2,\ddy + 3) -- (\ddx + 3,\ddy + 3)%
+ -- (\ddx + 3,\ddy + 2) -- cycle;
+%%-----middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Dlm]%
+(\ddx + 0,\ddy + 1) -- (\ddx + 0,\ddy + 2) -- (\ddx + 1,\ddy + 2)%
+ -- (\ddx + 1,\ddy + 1)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Dmm]%
+(\ddx + 1,\ddy + 1) -- (\ddx + 1,\ddy + 2) -- (\ddx + 2,\ddy + 2)%
+ -- (\ddx + 2,\ddy + 1) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Drm]%
+(\ddx + 2,\ddy + 1) -- (\ddx + 2,\ddy + 2) -- (\ddx + 3,\ddy + 2)%
+ -- (\ddx + 3,\ddy + 1) -- cycle;
+%%----bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Dlb]%
+(\ddx + 0,\ddy + 0) -- (\ddx + 0,\ddy + 1) -- (\ddx + 1,\ddy + 1)%
+ -- (\ddx + 1,\ddy + 0)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Dmb]%
+(\ddx + 1,\ddy + 0) -- (\ddx + 1,\ddy + 1) -- (\ddx + 2,\ddy + 1)%
+ -- (\ddx + 2,\ddy + 0) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Drb]%
+(\ddx + 2,\ddy + 0) -- (\ddx + 2,\ddy + 1) -- (\ddx + 3,\ddy + 1)%
+ -- (\ddx + 3,\ddy + 0) -- cycle;
+}
+%%-----------------------
+\newcommand{\FlatFront}{%
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Flt]%
+(0,2) -- (0, 3) -- (1,3) -- (1,2)  -- cycle;
+%%
+\draw[line join=round,line cap=round,ultra thick,fill=\Fmt]%
+(1,2) -- (1, 3) -- (2,3) -- (2,2) -- cycle;
+%%
+\draw[line join=round,line cap=round,ultra thick,fill=\Frt]%
+(2,2) -- (2, 3) -- (3,3) -- (3,2) -- cycle;
+%%-----middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Flm]%
+(0,1) -- (0, 2) -- (1,2) -- (1,1)  -- cycle;
+%%
+\draw[line join=round,line cap=round,ultra thick,fill=\Fmm]%
+(1,1) -- (1, 2) -- (2,2) -- (2,1) -- cycle;
+%%
+\draw[line join=round,line cap=round,ultra thick,fill=\Frm]%
+(2,1) -- (2, 2) -- (3,2) -- (3,1) -- cycle;
+%%----bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Flb]%
+(0,0) -- (0, 1) -- (1,1) -- (1,0)  -- cycle;
+%%
+\draw[line join=round,line cap=round,ultra thick,fill=\Fmb]%
+(1,0) -- (1, 1) -- (2,1) -- (2,0) -- cycle;
+%%
+\draw[line join=round,line cap=round,ultra thick,fill=\Frb]%
+(2,0) -- (2, 1) -- (3,1) -- (3,0) -- cycle;
+}
+%%-------------------------
+\newcommand{\FlatBack}[2]{%
+\pgfmathsetmacro{\bx}{#1}%
+\pgfmathsetmacro{\by}{#2}%
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Blt]%
+(\bx + 0,\by + 2) -- (\bx + 0,\by + 3) -- (\bx + 1,\by + 3)%
+ -- (\bx + 1,\by + 2)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Bmt]%
+(\bx + 1,\by + 2) -- (\bx + 1,\by + 3) -- (\bx + 2,\by + 3)%
+ -- (\bx + 2,\by + 2) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Brt]%
+(\bx + 2,\by + 2) -- (\bx + 2,\by + 3) -- (\bx + 3,\by + 3)%
+ -- (\bx + 3,\by + 2) -- cycle;
+%%-----middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Blm]%
+(\bx + 0,\by + 1) -- (\bx + 0,\by + 2) -- (\bx + 1,\by + 2)%
+ -- (\bx + 1,\by + 1)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Bmm]%
+(\bx + 1,\by + 1) -- (\bx + 1,\by + 2) -- (\bx + 2,\by + 2)%
+ -- (\bx + 2,\by + 1) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Brm]%
+(\bx + 2,\by + 1) -- (\bx + 2,\by + 2) -- (\bx + 3,\by + 2)%
+ -- (\bx + 3,\by + 1) -- cycle;
+%%----bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Blb]%
+(\bx + 0,\by + 0) -- (\bx + 0,\by + 1) -- (\bx + 1,\by + 1)%
+ -- (\bx + 1,\by + 0)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Bmb]%
+(\bx + 1,\by + 0) -- (\bx + 1,\by + 1) -- (\bx + 2,\by + 1)%
+ -- (\bx + 2,\by + 0) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Brb]%
+(\bx + 2,\by + 0) -- (\bx + 2,\by + 1) -- (\bx + 3,\by + 1)%
+ -- (\bx + 3,\by + 0) -- cycle;
+}
+%%-------------------------
+\newcommand{\FlatLeft}[2]{%
+\pgfmathsetmacro{\lx}{#1}%
+\pgfmathsetmacro{\ly}{#2}%
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Llt]%
+(\lx + 0,2) -- (\lx + 0, 3) -- (\lx + 1,3) -- (\lx + 1,2)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lmt]%
+(\lx + 1,2) -- (\lx + 1, 3) -- (\lx + 2,3) -- (\lx + 2,2) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lrt]%
+(\lx + 2,2) -- (\lx + 2, 3) -- (\lx + 3,3) -- (\lx + 3,2) -- cycle;
+%%-----middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Llm]%
+(\lx + 0,1) -- (\lx + 0, 2) -- (\lx + 1,2) -- (\lx + 1,1)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lmm]%
+(\lx + 1,1) -- (\lx + 1, 2) -- (\lx + 2,2) -- (\lx + 2,1) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lrm]%
+(\lx + 2,1) -- (\lx + 2, 2) -- (\lx + 3,2) -- (\lx + 3,1) -- cycle;
+%%----bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Llb]%
+(\lx + 0,0) -- (\lx + 0, 1) -- (\lx + 1,1) -- (\lx + 1,0)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lmb]%
+(\lx + 1,0) -- (\lx + 1, 1) -- (\lx + 2,1) -- (\lx + 2,0) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Lrb]%
+(\lx + 2,0) -- (\lx + 2, 1) -- (\lx + 3,1) -- (\lx + 3,0) -- cycle;
+}
+%%--------------------------
+\newcommand{\FlatRight}[2]{%
+\pgfmathsetmacro{\rx}{#1}% %3
+\pgfmathsetmacro{\ry}{#2}% %0
+%%---top row
+\draw[line join=round,line cap=round,ultra thick,fill=\Rlt]%
+(\rx + 0,2) -- (\rx + 0, 3) -- (\rx + 1,3) -- (\rx + 1,2)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rmt]%
+(\rx + 1,2) -- (\rx + 1, 3) -- (\rx + 2,3) -- (\rx + 2,2) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rrt]%
+(\rx + 2,2) -- (\rx + 2, 3) -- (\rx + 3,3) -- (\rx + 3,2) -- cycle;
+%%-----middle row
+\draw[line join=round,line cap=round,ultra thick,fill=\Rlm]%
+(\rx + 0,1) -- (\rx + 0, 2) -- (\rx + 1,2) -- (\rx + 1,1)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rmm]%
+(\rx + 1,1) -- (\rx + 1, 2) -- (\rx + 2,2) -- (\rx + 2,1) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rrm]%
+(\rx + 2,1) -- (\rx + 2, 2) -- (\rx + 3,2) -- (\rx + 3,1) -- cycle;
+%%----bottom row
+\draw[line join=round,line cap=round,ultra thick,fill=\Rlb]%
+(\rx + 0,0) -- (\rx + 0, 1) -- (\rx + 1,1) -- (\rx + 1,0)  -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rmb]%
+(\rx + 1,0) -- (\rx + 1, 1) -- (\rx + 2,1) -- (\rx + 2,0) -- cycle;
+\draw[line join=round,line cap=round,ultra thick,fill=\Rrb]%
+(\rx + 2,0) -- (\rx + 2, 1) -- (\rx + 3,1) -- (\rx + 3,0) -- cycle;
+}
+%    \end{macrocode}
+%
+%  \begin{macro}{\DrawRubikFlat}
+%  Draws a standard flat representation of the Rubik's 
+%  cube (colours only)
+%    \begin{macrocode}
+\newcommand{\DrawRubikFlat}{%
+  \FlatUp{0}{3}%
+  \FlatDown{0}{-3}%
+  \FlatLeft{-3}{0}%
+  \FlatFront%
+  \FlatRight{3}{0}%
+  \FlatBack{6}{0}%
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\DrawRubikCubeFlat}
+%  Draws a Rubik's  cube together with the three hidden faces
+%   (colours only)
+%    \begin{macrocode}
+\newcommand{\DrawRubikCubeFlat}{%
+  \DrawRubikCube%
+  \FlatDown{0}{-3}%
+  \FlatLeft{-3}{0}%
+  \FlatBack{4}{1}%
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%   \subsection{    SideBar commands}
+%
+%  SideBar commands draw narrow bars of colour indicating  the 
+%  side colours of each of the cubies forming the side of
+%  a given layer (face).
+%
+%  \begin{macro}{\RubikSideBarWidth}
+%  \begin{macro}{\RubikSideBarLength} 
+%  \begin{macro}{\RubikSideBarSep}
+% These three commands allow the user to set the Width, Length 
+% and Separation parameters for the sidebar (in decimal values, 
+% where 1 is equivalent to the length of the side of a cubie).
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%    \begin{macrocode}
+\newcommand{\RubikSideBarWidth}[1]{\pgfmathsetmacro{\bw}{#1}}
+\newcommand{\RubikSideBarLength}[1]{\pgfmathsetmacro{\bl}{#1}}
+\newcommand{\RubikSideBarSep}[1]{\pgfmathsetmacro{\bs}{#1}}
+%    \end{macrocode}
+% We first set some default values
+%    \begin{macrocode}
+\RubikSideBarWidth{0.3}%
+\RubikSideBarLength{1}%
+\RubikSideBarSep{0.3}%
+%    \end{macrocode}
+%
+%
+% \subsubsection{    Allocating  a colour to a single cubie sidebar}
+% 
+% \begin{macro}{\side@barT}
+% \begin{macro}{\side@barB}
+% \begin{macro}{\side@barL}
+% \begin{macro}{\side@barR}
+% Internal commands.
+% Full length face SideBars are really multiple instances of 
+% single cubie bars, 
+% each of which is drawn  using one of four internal SideBar 
+% commands---one for each of the sides which we shall 
+% call Top, Bottom,  Left, Right.
+% Each SideBar command  takes two arguments: one for cubie position 
+% \marg{$ 1 \mid 2 \mid 3$} and  one for 
+% the colour-code \marg{$ R \mid O \mid Y \mid G \mid B \mid W \mid X $}.
+%
+% \textsc{example}: the following command allocates a colour to a single 
+% cubie sidebar on the Left of a Rubik face: 
+%  \begin{quote}
+%     \cmd{\side@barL}\marg{cubie-position}\marg{colour-code}
+%  \end{quote}
+% There are three cubie positions on  each of the four sides 
+% of a face, and these 
+% are numbered 1 to 3 starting from the bottom left corner (1,1). 
+% The SideBar command  also implements the set (or default) 
+% Length (\cmd{\bl}), Width (\cmd{\bw}) and Separation (\cmd{\bs}) 
+% values mentioned above. \cmd{\blh} = Half \cmd{\bl} = \cmd{\bl}/2.
+% 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 Draw command for  each bar rectangle 
+%    is botton Left corner of the bar =(\cmd{\dx},\cmd{\dy})
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%    \begin{macrocode}
+\newcommand{\side@barL}[2]{%
+%% #1 = cubie possn no, #2 = colour
+\pgfmathsetmacro{\blh}{\bl*(0.5)}%
+\pgfmathsetmacro{\dx}{0 - \bs - \bw}%
+\pgfmathsetmacro{\dy}{#1-1+0.5-\blh}%
+\draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bl) 
+  -- (\dx+\bw,\dy+\bl) -- (\dx+\bw,\dy) -- cycle;
+}
+\newcommand{\side@barR}[2]{%
+%% #1 = cubie possn no, #2 = colour
+\pgfmathsetmacro{\blh}{\bl*(0.5)}%
+\pgfmathsetmacro{\dx}{3 + \bs}%
+\pgfmathsetmacro{\dy}{#1 -1+0.5-\blh}%
+\draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bl)
+  -- (\dx+\bw,\dy+\bl) -- (\dx+\bw,\dy) -- cycle;
+}
+\newcommand{\side@barT}[2]{%
+%% #1 = cubie possn no, #2 = colour
+\pgfmathsetmacro{\blh}{\bl*(0.5)}%
+\pgfmathsetmacro{\dx}{#1 -1+0.5-\blh}%
+\pgfmathsetmacro{\dy}{3 +\bs}%
+\draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bw)
+  -- (\dx+\bl,\dy+\bw) -- (\dx+\bl,\dy) -- cycle;
+}
+\newcommand{\side@barB}[2]{%
+%% #1 = cubie possn no, #2 = colour
+\pgfmathsetmacro{\blh}{\bl*(0.5)}%
+\pgfmathsetmacro{\dx}{#1 -1+0.5-\blh}%
+\pgfmathsetmacro{\dy}{0 -\bs-\bw}%
+\draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bw)
+  -- (\dx+\bl,\dy+\bw) -- (\dx+\bl,\dy) -- cycle;
+}
+%    \end{macrocode}
+%
+%
+% \subsubsection{    Drawing a single cubie sidebar}
+% 
+%  \begin{macro}{\DrawRubikLayerSideX$_1$X$_2$X$_3$}
+% This command draws the sidebars using the above \cmd{\sidebar} command.
+% The X$_1$X$_2$X$_2$ parameters refer to the  options Left, Middle, 
+% Right, Top, Equator, 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 $\langle T\mid E \mid  B\rangle$
+%  {\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.
+% \end{quote}
+% For example, the following command
+% \begin{quote}
+%   \cmd{\DrawRubikLayerSideLTy\{G\}}
+% \end{quote}
+% draws a Green sidebar above the Top Left cubie. 
+% \end{macro}
+% 
+% \begin{macrocode}
+%%---Left side
+\newcommand{\DrawRubikLayerSideLTx}[1]{\side@barL{3}{#1}}
+\newcommand{\DrawRubikLayerSideLEx}[1]{\side@barL{2}{#1}}
+\newcommand{\DrawRubikLayerSideLE}[1]{\side@barL{2}{#1}}
+\newcommand{\DrawRubikLayerSideLBx}[1]{\side@barL{1}{#1}}
+%---Right side
+\newcommand{\DrawRubikLayerSideRTx}[1]{\side@barR{3}{#1}}
+\newcommand{\DrawRubikLayerSideREx}[1]{\side@barR{2}{#1}}
+\newcommand{\DrawRubikLayerSideRE}[1]{\side@barR{2}{#1}}
+\newcommand{\DrawRubikLayerSideRBx}[1]{\side@barR{1}{#1}}
+%---Top side
+\newcommand{\DrawRubikLayerSideLTy}[1]{\side@barT{1}{#1}}
+\newcommand{\DrawRubikLayerSideMTy}[1]{\side@barT{2}{#1}}
+\newcommand{\DrawRubikLayerSideMT}[1]{\side@barT{2}{#1}}
+\newcommand{\DrawRubikLayerSideRTy}[1]{\side@barT{3}{#1}}
+%---Bottom side
+\newcommand{\DrawRubikLayerSideLBy}[1]{\side@barB{1}{#1}}
+\newcommand{\DrawRubikLayerSideMBy}[1]{\side@barB{2}{#1}}
+\newcommand{\DrawRubikLayerSideMB}[1]{\side@barB{2}{#1}}
+\newcommand{\DrawRubikLayerSideRBy}[1]{\side@barB{3}{#1}}
+%    \end{macrocode}
+%
+%
+%  \subsubsection{    Drawing multiple cubie  sidebars}
+%
+%    \begin{macro}{\DrawRubikLayerSideT}
+%    \begin{macro}{\DrawRubikLayerSideB}
+%    \begin{macro}{\DrawRubikLayerSideL}
+%    \begin{macro}{\DrawRubikLayerSideR}
+%  These commands allow the drawing of  3 small sidebars along 
+%  one particular side (Top, Bottom, Left, Right), as indicated 
+%  by the appended T, B, L, R letter code.
+%  Each command takes three ordered colour arguments, which are ordered 
+%  either from left to right (the T and B forms), or from top to bottom
+%  (the L and R forms)
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%   \begin{macrocode}
+%%--Top side---
+\newcommand{\DrawRubikLayerSideT}[3]{%
+  \DrawRubikLayerSideLTy{#1}%
+  \DrawRubikLayerSideMTy{#2}%
+  \DrawRubikLayerSideRTy{#3}%
+}
+%%--Bottom side---
+\newcommand{\DrawRubikLayerSideB}[3]{%
+  \DrawRubikLayerSideLBy{#1}%
+  \DrawRubikLayerSideMBy{#2}%
+  \DrawRubikLayerSideRBy{#3}%
+}
+%%--Left side--------
+%% colours run vertically DOWN
+\newcommand{\DrawRubikLayerSideL}[3]{%
+  \DrawRubikLayerSideLTx{#1}%
+  \DrawRubikLayerSideLEx{#2}%
+  \DrawRubikLayerSideLBx{#3}%
+}
+%%--Right side--------
+%% colours run vertically DOWN
+\newcommand{\DrawRubikLayerSideR}[3]{%
+  \DrawRubikLayerSideRTx{#1}%
+  \DrawRubikLayerSideREx{#2}%
+  \DrawRubikLayerSideRBx{#3}%
+}
+%    \end{macrocode}
+%
+%  \begin{macro}{\DrawRubikLayerSideLR}
+% This command draws six cubie sidebars, three on each side, drawn in (L, R)
+%  pairs. The command takes six colour arguments, ordered in pairs, 
+%  as shown in the following example.
+% \begin{quote}
+%\begin{verbatim}
+%  \DrawRubikLayerSideLR{G}   {G}
+%                       {R}   {B}
+%                       {Y}   {B}
+%\end{verbatim}
+%  \end{quote}
+%  \begin{macrocode}
+\newcommand{\DrawRubikLayerSideLR}[6]{%
+  \DrawRubikLayerSideLTx{#1}%
+  \DrawRubikLayerSideRTx{#2}%
+  \DrawRubikLayerSideLEx{#3}%
+  \DrawRubikLayerSideREx{#4}%
+  \DrawRubikLayerSideLBx{#5}%
+  \DrawRubikLayerSideRBx{#6}%
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%    \subsection{    NCube command}
+%
+%  \textsc{history}: The essence of this command was originally developed by Peter Bartal 
+%  as his command \cmd{\rubikcube} (see Bartal,
+%  2011). We have modified it, as follows (June 2012):
+%  \newline\strut\hspace{\parindent}(1) adjusted  to use the TikZ \cmd{\pgfmathsetmacro\{\}\{\}} command,
+%  \newline\strut\hspace{\parindent}(2)  renamed to \cmd{\DrawNCubeAll}.
+%
+%    \begin{macro}{\DrawNCubeAll}
+% {\noindent}This command draws a solved NxNxN Rubik's cube from the RightUp viewpoint.
+% All cubies on a given face have the same colour. 
+% The command takes four ordered  arguments, as follows:
+% \newline\strut\hspace{\parindent}\#1 = number of cubies ($n>0$) along each side,
+% \newline\strut\hspace{\parindent}\#2, \#3, \#4 = colors of the visible faces (in X,Y,Z order);
+%  X=Right face  colour, Y=Up face colour, Z=Front face colour.
+%
+% \begin{macrocode}
+\newcommand{\DrawNCubeAll}[4]{%
+   \pgfmathsetmacro{\ncubes}{#1-1}%
+%% need to subtract 1 from the given number of cubies per side 
+%% to avoid the origin of the initial cube to be displaced
+    \foreach \x in {0,...,\ncubes}{%
+      \foreach \y in {0,...,\ncubes}{%
+        \foreach \z in {0,...,\ncubes}{%
+          \cube@dxdydz{1}{#2}{#3}{#4}{\x}{\y}{\z}% 
+  }}}}
+%    \end{macrocode}
+%    \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), and also by Peter Grill (see below).
+%
+%  The cube need not be in the origin, the distances of 
+% the Down-behind [L] corner from 
+% the origin are taken as parameters.
+% The command takes 7 ordered arguments:
+% \newline\strut\hspace{\parindent}1 - length of an edge 
+% \newline\strut\hspace{\parindent}2 - color of the X face (Right) (RWDN)
+% \newline\strut\hspace{\parindent}3 - color of the Y face (Up)    (RWDN)
+% \newline\strut\hspace{\parindent}4 - color of the Z face (Front) (RWDN)
+% \newline\strut\hspace{\parindent}5 - x-position in space
+% \newline\strut\hspace{\parindent}6 - y-position in space
+% \newline\strut\hspace{\parindent}7 - z-position in space
+%
+% \textsc{usage}:  |\cube@dxdydz{1}{cX}{cY}{cZ}{x}{y}{z}|
+%
+% {\noindent}The original code
+%   |\pgfmathparse{#1+#5}\let\dy\pgfmathresult| 
+% {\newline} was changed  to the more intuitive  |\pgfmathsetmacro{\dx}{#1+#5}|
+% (suggested by Peter Grill 2011).
+%
+% \textsc{changes}: RWD Nickalls (2012): 
+% (1) added the [line join=round,line cap=round] 
+% options to  each of the TikZ  `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).
+%    \begin{macrocode}
+\newcommand{\cube@dxdydz}[7]{%
+   \pgfmathsetmacro{\dx}{#1+#5}% 
+%% calculates the 'displacement' (distance from the origin) of the 
+%% far corners of the cube along the x axis from the arguments
+   \pgfmathsetmacro{\dy}{#1+#6}%
+%% calculates the 'displacement' (distance from the origin) of the 
+%% far corners of the cube along the y axis from the arguments
+   \pgfmathsetmacro{\dz}{#1+#7}%
+%% calculates the 'displacement' (distance from the origin) of the 
+%% far corners of the cube along the z axis from the arguments
+%% Draw FRONT face   (using the X colour = #4)
+    \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
+%% 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;
+%% Draw RIGHT face   (using the X colour = #2)
+ \draw[line join=round,line cap=round,ultra thick,fill=#2]%
+ (\dx,#6,\dz) -- (\dx,#6,#7) -- (\dx,\dy,#7) -- (\dx,\dy,\dz) -- cycle;
+    }
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+%  \subsection{    Drawing single cubies}
+%
+%  \begin{macro}{\Cubiedx}
+%  \begin{macro}{\Cubiedy}
+%  These two commands set the value of the two length parameters
+%  \texttt{cx} and \texttt{cy}, and allow the user to vary the size 
+%  (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} since these have been 
+% used before (see above). However we use \texttt{dx}, \texttt{dy} in the  command names
+% since these will be more  readily understood by the user.
+%    \begin{macrocode}
+\newcommand{\Cubiedx}[1]{\pgfmathsetmacro{\cx}{#1}}
+\newcommand{\Cubiedy}[1]{\pgfmathsetmacro{\cy}{#1}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+% We now set the default values (cx=cy=0.4)
+%    \begin{macrocode}
+\Cubiedx{0.4}
+\Cubiedy{0.4}
+%    \end{macrocode}
+%
+%
+%  \begin{macro}{\DrawCubieRU}
+%  \begin{macro}{\DrawCubieRD}
+%  \begin{macro}{\DrawCubieLU}
+%  \begin{macro}{\DrawCubieLD}
+% These four commands draw a single cubie from the RightUp, RightDown, 
+% LeftUp, LeftDown viewpoint. 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).
+% \newline\textsc{format}: \cmd{\DrawCubieRU}\marg{colourX}\marg{colourY}\marg{colourZ}
+% \newline\textsc{usage}: |\DrawCubieRU{G}{B}{W}|
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \begin{macrocode}
+\newcommand{\DrawCubieRU}[3]{%
+%% Front face (z)
+\draw[line join=round,line cap=round,ultra thick,fill=#3]%
+ (0,0) -- (0, 1) -- (1, 1) -- (1,0) -- cycle;
+%% Up face(y)
+\draw[line join=round,line cap=round,ultra thick,fill=#2]%
+ (0,1) -- (\cx, 1+\cy) -- (1+\cx,1+\cy) -- (1,1) -- cycle;
+%% Right face(x)
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+ (1,0) -- (1,1) -- (1+\cx,1+\cy) -- (1+\cx, \cy) -- cycle;
+}
+\newcommand{\DrawCubieRD}[3]{%
+%% Front face (z)
+\draw[line join=round,line cap=round,ultra thick,fill=#3]%
+ (0,0) -- (0, 1) -- (1, 1) -- (1,0) -- cycle;
+%% Down face (y)
+\draw[line join=round,line cap=round,ultra thick,fill=#2]%
+ (\cx,-\cy) -- (0, 0) -- (1,0) -- (1+\cx,-\cy) -- cycle;
+%% Right face (x)
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+ (1,0) -- (1,1) -- (1+\cx,-\cy+1) -- (1+\cx, -\cy) -- cycle;
+}
+\newcommand{\DrawCubieLD}[3]{%
+%% Front face (z)
+\draw[line join=round,line cap=round,ultra thick,fill=#3]%
+ (0,0) -- (0, 1) -- (1, 1) -- (1,0) -- cycle;
+%% Down face (y)
+\draw[line join=round,line cap=round,ultra thick,fill=#2]%
+ (-\cx,-\cy) -- (0, 0) -- (1,0) -- (1-\cx,-\cy) -- cycle;
+%% Left face (x)
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+ (-\cx,-\cy) -- (-\cx,-\cy+1) -- (0,1) -- (0,0) -- cycle;
+}
+\newcommand{\DrawCubieLU}[3]{%
+%% Front face (z)
+\draw[line join=round,line cap=round,ultra thick,fill=#3]%
+ (0,0) -- (0, 1) -- (1, 1) -- (1,0) -- cycle;
+%% Up face (y)
+\draw[line join=round,line cap=round,ultra thick,fill=#2]%
+ (-\cx,1+\cy) -- (1-\cx, 1+\cy) -- (1,1) -- (0,1) -- cycle;
+%% Left face (x)
+\draw[line join=round,line cap=round,ultra thick,fill=#1]%
+ (-\cx, \cy) -- (-\cx,\cy+1) -- (0,1) -- (0,0) -- cycle;
+}
+%    \end{macrocode}
+%
+%
+%  \subsection{    Text cubies}
+% 
+%  \begin{macro}{\textCubieRU}
+%  \begin{macro}{\textCubieRD}
+%  \begin{macro}{\textCubieLU}
+%  \begin{macro}{\textCubieLD}
+%  These four commands draw a single `text' cubie from the RightUp, RightDown, 
+%  LeftUp, LeftDown viewpoint. 
+%  They are `text' forms of the DrawCubie' versions described above.
+%  Their size is scaled to be suitable for use with  10--12 point fonts.  
+%
+%  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).
+% \newline\textsc{format}: \cmd{\textCubieRU}\marg{colourX}\marg{colourY}\marg{colourZ}
+% \newline\textsc{usage}: |\textCubieRU{G}{B}{W}|
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \begin{macrocode}
+\newcommand{\textCubieRU}[3]{%
+\begin{minipage}{0.66cm}
+\centering
+\begin{tikzpicture}[scale=0.5]
+\Cubiedx{0.4}\Cubiedy{0.4}
+\DrawCubieRU{#1}{#2}{#3}
+\end{tikzpicture}
+\end{minipage}
+}
+\newcommand{\textCubieRD}[3]{%
+\begin{minipage}{0.66cm}
+\centering
+\begin{tikzpicture}[scale=0.5]
+\Cubiedx{0.4}\Cubiedy{0.4}
+\DrawCubieRD{#1}{#2}{#3}
+\end{tikzpicture}
+\end{minipage}
+}
+\newcommand{\textCubieLD}[3]{%
+\begin{minipage}{0.66cm}
+\centering
+\begin{tikzpicture}[scale=0.5]
+\Cubiedx{0.4}\Cubiedy{0.4}
+\DrawCubieLD{#1}{#2}{#3}
+\end{tikzpicture}
+\end{minipage}
+}
+\newcommand{\textCubieLU}[3]{%
+\begin{minipage}{0.66cm}
+\centering
+\begin{tikzpicture}[scale=0.5]
+\Cubiedx{0.4}\Cubiedy{0.4}
+\DrawCubieLU{#1}{#2}{#3}
+\end{tikzpicture}
+\end{minipage}
+}
+%    \end{macrocode}
+%
+%
+%  \subsection{    Rotation commands --- face and slice}
+%
+% \textsc{notation}: We require a special notation to denote the 
+% various Rubik rotations (denoted 
+% by the stem rr). These rotations can be denoted either  using a letter code
+% say, \cmd{\rrR} for a Right  face rotation, or by the equivalent hieroglyph
+% denoted as \cmd{\rrhR}  (Rubik rotation hieroglyph Right) etc.
+% Commands such as \cmd{\RubikXXXX} typeset a pair of rr and rrh vertically.
+% Commands such as \cmd{\textRubikXXXX} typeset  the pair rr and rrh horizontally 
+% (ie  a sort of `text' mode).
+%
+% 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 pgfmanual2012  page p146 (\S 14.8)).
+%
+%  The presence of small overfilled hboxes associated with these squares
+% were originally checked using the ltugboat.cls, and all fixed mainly
+% by setting the associated  minipages $\rightarrow$ width = 0.6cm, 
+%  and using TKZ scale=0.5.
+% NOTE: do not use a trailing |%|  after each |\end{tikzpicture}| 
+% as we actually need a small space to appear when used in text.
+%
+%
+%   \begin{macro}{\DrawNotationBox}
+% This command draws the surrounding square box of  all the hieroglyphs.
+% Note that we start at (0,0) and draw to the final point 
+% in order to make a nice corner join.
+%
+%   \begin{macrocode}
+\newcommand{\DrawNotationBox}{%
+  \draw [thick] (0,0) -- (0,1) -- (1,1) -- (1,0) -- (0,0) -- (0,1)%
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+% We now define  a number of points and line-segments inside the square 
+% (eg.; \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.
+% 
+%\begin{macrocode}
+\pgfmathsetmacro{\sd}{0.25} % horiz space 
+\pgfmathsetmacro{\sdd}{2*\sd} 
+\pgfmathsetmacro{\sddd}{3*\sd}
+\pgfmathsetmacro{\sh}{0.6} % height
+\pgfmathsetmacro{\sb}{0.2} % base
+\pgfmathsetmacro{\sbh}{\sb + \sh} % UP
+\pgfmathsetmacro{\scx}{\sdd+0.2} % Start of CircleX
+\pgfmathsetmacro{\scy}{\sd*2/3}  % Start of CircleY
+\pgfmathsetmacro{\sqcx}{\scx-0.13} %% SQuare CenterX
+\pgfmathsetmacro{\sqcy}{\scy+0.25} %% SQuare CenterY
+%    \end{macrocode}
+%
+%
+%  \subsubsection{     Rotation B}
+%
+%  \begin{macro}{\rrB}
+%  \begin{macro}{\SquareB}
+%  \begin{macro}{\rrhB}
+%  \begin{macro}{\RubikB}
+%  \begin{macro}{\textRubikB}
+%  These commands  all draw forms which denote the B rotation.
+%  Not visible from the front.
+% \begin{macrocode}
+\newcommand{\rrB}{\@rr{B}}
+\newcommand{\SquareB}{\@SquareLetter{\rrB}}
+\newcommand{\rrhB}{\raisebox{-0.25mm}{\SquareB}\,}
+\newcommand{\RubikB}{\raisebox{\@hRubik}{\SquareB}\,}
+\newcommand{\textRubikB}{\rrhB\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Bp}
+%
+%  \begin{macro}{\rrBp}
+%  \begin{macro}{\SquareBp}
+%  \begin{macro}{\rrhBp}
+%  \begin{macro}{\RubikBp}
+%  \begin{macro}{\textRubikBp}
+%  These commands  all draw forms which denote the Bp rotation.
+%  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\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Bw}
+%
+%  \begin{macro}{\rrBw}
+%  \begin{macro}{\SquareBw}
+%  \begin{macro}{\rrhBw}
+%  \begin{macro}{\RubikBw}
+%  \begin{macro}{\textRubikBw}
+%  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\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Bwp}
+%
+%  \begin{macro}{\rrBwp}
+%  \begin{macro}{\SquareBwp}
+%  \begin{macro}{\rrhBwp}
+%  \begin{macro}{\RubikBwp}
+%  \begin{macro}{\textRubikBwp}
+%  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\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Bs}
+%
+%  \begin{macro}{\rrBs}
+%  \begin{macro}{\SquareBs}
+%  \begin{macro}{\rrhBs}
+%  \begin{macro}{\RubikBs}
+%  \begin{macro}{\textRubikBs}
+%  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\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Bsp}
+%
+%  \begin{macro}{\rrBsp}
+%  \begin{macro}{\SquareBsp}
+%  \begin{macro}{\rrhBsp}
+%  \begin{macro}{\RubikBsp}
+%  \begin{macro}{\textRubikBsp}
+%  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\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Ba}
+%
+%  \begin{macro}{\rrBa}
+%  \begin{macro}{\SquareBa}
+%  \begin{macro}{\rrhBa}
+%  \begin{macro}{\RubikBa}
+%  \begin{macro}{\textRubikBa}
+%  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\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Bap}
+%
+%  \begin{macro}{\rrBap}
+%  \begin{macro}{\SquareBap}
+%  \begin{macro}{\rrhBap}
+%  \begin{macro}{\RubikBap}
+%  \begin{macro}{\textRubikBap}
+%  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\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation D}
+%
+%  \begin{macro}{\rrD}
+%  \begin{macro}{\SquareD}
+%  \begin{macro}{\rrhD}
+%  \begin{macro}{\RubikD}
+%  \begin{macro}{\textRubikD}
+%  These commands  all draw forms which denote the D rotation.
+% \begin{macrocode}
+\newcommand{\rrD}{\textbf{\textsf{D}}}
+%%
+\newcommand{\SquareD}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick]     (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick, ->]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%%
+}
+\newcommand{\rrhD}{\raisebox{-0.333\height}{\SquareD}\,}
+%%
+\newcommand{\RubikD}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareD\\
+\rrD
+\end{minipage}%
+}
+\newcommand{\textRubikD}{\rrD\,\rrhD}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Dp}
+%
+%  \begin{macro}{\rrDp}
+%  \begin{macro}{\SquareDp}
+%  \begin{macro}{\rrhDp}
+%  \begin{macro}{\RubikDp}
+%  \begin{macro}{\textRubikDp}
+%  These commands  all draw forms which denote the Dp rotation.
+% \begin{macrocode}
+\newcommand{\rrDp}{\textbf{\textsf{D}$^\prime$}}
+%%
+\newcommand{\SquareDp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick]     (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick]     (\sb,\sdd)  -- (\sbh, \sdd);
+\draw [thick, <-] (\sb,\sd)   -- (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhDp}{\raisebox{-0.333\height}{\SquareDp}\,}
+%%
+\newcommand{\RubikDp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareDp\\
+\rrDp
+\end{minipage}%
+}
+\newcommand{\textRubikDp}{\rrDp\,\rrhDp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Dw}
+%
+%  \begin{macro}{\rrDw}
+%  \begin{macro}{\SquareDw}
+%  \begin{macro}{\rrhDw}
+%  \begin{macro}{\RubikDw}
+%  \begin{macro}{\textRubikDw}
+%  These commands  all draw forms which denote the Dw rotation.
+% \begin{macrocode}
+\newcommand{\rrDw}{\textbf{\textsf{D\footnotesize{w}}}}
+%%
+\newcommand{\SquareDw}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick]     (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick, ->] (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick, ->] (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhDw}{\raisebox{-0.333\height}{\SquareDw}\,}
+%%
+\newcommand{\RubikDw}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareDw\\
+\rrDw
+\end{minipage}%
+}
+\newcommand{\textRubikDw}{\rrDw\,\rrhDw}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Dwp}
+%
+%  \begin{macro}{\rrDwp}
+%  \begin{macro}{\SquareDwp}
+%  \begin{macro}{\rrhDwp}
+%  \begin{macro}{\RubikDwp}
+%  \begin{macro}{\textRubikDwp}
+%  These commands  all draw forms which denote the Dwp rotation.
+% \begin{macrocode}
+\newcommand{\rrDwp}{\textbf{\textsf{D\footnotesize{w}}$^\prime$}}
+%%
+\newcommand{\SquareDwp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick]     (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick, <-] (\sb,\sdd)  -- (\sbh, \sdd);
+\draw [thick, <-] (\sb,\sd)   -- (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhDwp}{\raisebox{-0.333\height}{\SquareDwp}\,}
+%%
+\newcommand{\RubikDwp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareDwp\\
+\rrDwp
+\end{minipage}%
+}
+\newcommand{\textRubikDwp}{\rrDwp\,\rrhDwp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Ds}
+%
+%  \begin{macro}{\rrDs}
+%  \begin{macro}{\SquareDs}
+%  \begin{macro}{\rrhDs}
+%  \begin{macro}{\RubikDs}
+%  \begin{macro}{\textRubikDs}
+%  These commands  all draw forms which denote the Ds rotation.
+% \begin{macrocode}
+\newcommand{\rrDs}{\@rrs{D}}
+%%
+\newcommand{\SquareDs}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, ->] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick]     (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick, ->]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhDs}{\raisebox{-0.333\height}{\SquareDs}\,}
+%%
+\newcommand{\RubikDs}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareDs\\
+\rrDs
+\end{minipage}%
+}
+\newcommand{\textRubikDs}{\rrDs\,\rrhDs}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Dsp}
+%
+%  \begin{macro}{\rrDsp}
+%  \begin{macro}{\SquareDsp}
+%  \begin{macro}{\rrhDsp}
+%  \begin{macro}{\RubikDsp}
+%  \begin{macro}{\textRubikDsp}
+%  These commands  all draw forms which denote the Dsp rotation.
+% \begin{macrocode}
+\newcommand{\rrDsp}{\@rrsp{D}}
+%%
+\newcommand{\SquareDsp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, <-] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick]     (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick, <-]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhDsp}{\raisebox{-0.333\height}{\SquareDsp}\,}
+%%
+\newcommand{\RubikDsp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareDsp\\
+\rrDsp
+\end{minipage}%
+}
+\newcommand{\textRubikDsp}{\rrDsp\,\rrhDsp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Da} 
+%
+%  \begin{macro}{\rrDa}
+%  \begin{macro}{\SquareDa}
+%  \begin{macro}{\rrhDa}
+%  \begin{macro}{\RubikDa}
+%  \begin{macro}{\textRubikDa}
+%  These commands  all draw forms which denote the Da rotation.
+% \begin{macrocode}
+\newcommand{\rrDa}{\@rra{D}}
+%%
+\newcommand{\SquareDa}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, <-] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick]     (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick, ->]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhDa}{\raisebox{-0.333\height}{\SquareDa}\,}
+%%
+\newcommand{\RubikDa}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareDa\\
+\rrDa
+\end{minipage}%
+}
+\newcommand{\textRubikDa}{\rrDa\,\rrhDa}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Dap} 
+%
+%  \begin{macro}{\rrDap}
+%  \begin{macro}{\SquareDap}
+%  \begin{macro}{\rrhDap}
+%  \begin{macro}{\RubikDap}
+%  \begin{macro}{\textRubikDap}
+%  These commands  all draw forms which denote the Dap rotation.
+% \begin{macrocode}
+\newcommand{\rrDap}{\@rrap{D}}
+%%
+\newcommand{\SquareDap}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, ->] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick]     (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick, <-]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhDap}{\raisebox{-0.333\height}{\SquareDap}\,}
+%%
+\newcommand{\RubikDap}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareDap\\
+\rrDap
+\end{minipage}%
+}
+\newcommand{\textRubikDap}{\rrDap\,\rrhDap}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation E}
+%
+%  \begin{macro}{\rrE}
+%  \begin{macro}{\SquareE}
+%  \begin{macro}{\rrhE}
+%  \begin{macro}{\RubikE}
+%  \begin{macro}{\textRubikE}
+%  These commands  all draw forms which denote the E rotation.
+% \begin{macrocode}
+\newcommand{\rrE}{\textbf{\textsf{E}}}
+%%
+\newcommand{\SquareE}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick, ->]     (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhE}{\raisebox{-0.333\height}{\SquareE}\,}
+%%
+\newcommand{\RubikE}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareE\\
+\rrE
+\end{minipage}%
+}
+\newcommand{\textRubikE}{\rrE\,\rrhE}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Ep}
+%
+%  \begin{macro}{\rrEp}
+%  \begin{macro}{\SquareEp}
+%  \begin{macro}{\rrhEp}
+%  \begin{macro}{\RubikEp}
+%  \begin{macro}{\textRubikEp}
+%  These commands  all draw forms which denote the Ep rotation.
+% \begin{macrocode}
+\newcommand{\rrEp}{\textbf{\textsf{E}$^\prime$}}
+%%
+\newcommand{\SquareEp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick, <-]     (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhEp}{\raisebox{-0.333\height}{\SquareEp}\,}
+%%
+\newcommand{\RubikEp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareEp\\
+\rrEp
+\end{minipage}%
+}
+\newcommand{\textRubikEp}{\rrEp\,\rrhEp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation F}
+%
+%  \begin{macro}{\rrF}
+%  \begin{macro}{\SquareF}
+%  \begin{macro}{\rrhF}
+%  \begin{macro}{\RubikF}
+%  \begin{macro}{\textRubikF}
+%  These commands  all draw forms which denote the F rotation.
+%  \begin{macrocode}
+\newcommand{\rrF}{\textbf{\textsf{F}}}
+%%
+\newcommand{\SquareF}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, <-] (\scx, \scy) arc[radius=0.35, start angle=-60, delta angle=290];
+\end{tikzpicture}%
+}
+\newcommand{\rrhF}{\raisebox{-0.333\height}{\SquareF}\,}
+%%
+\newcommand{\RubikF}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareF\\
+\rrF
+\end{minipage}%
+}
+\newcommand{\textRubikF}{\rrF\,\rrhF}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Fp}
+%
+%  \begin{macro}{\rrFp}
+%  \begin{macro}{\SquareFp}
+%  \begin{macro}{\rrhFp}
+%  \begin{macro}{\RubikFp}
+%  \begin{macro}{\textRubikFp}
+%  These commands  all draw forms which denote the Fp rotation.
+% \begin{macrocode}
+\newcommand{\rrFp}{\textbf{\textsf{F}$^\prime$}}
+%%
+\newcommand{\SquareFp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, ->] (\scx, \scy) arc[radius=0.35, start angle=-60, delta angle=290];
+\end{tikzpicture}%
+}
+\newcommand{\rrhFp}{\raisebox{-0.333\height}{\SquareFp}\,}
+%%
+\newcommand{\RubikFp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareFp\\
+\rrFp
+\end{minipage}%
+}
+\newcommand{\textRubikFp}{\rrFp\,\rrhFp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Fw}
+%
+%  \begin{macro}{\rrFw}
+%  \begin{macro}{\SquareFw}
+%  \begin{macro}{\rrhFw}
+%  \begin{macro}{\RubikFw}
+%  \begin{macro}{\textRubikFw}
+%  These commands  all draw forms which denote the Fw rotation.
+% \begin{macrocode}
+\newcommand{\rrFw}{\textbf{\textsf{F\footnotesize{w}}}}
+%%
+\newcommand{\SquareFw}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, <-] (\scx, \scy) arc[radius=0.35, start angle=-60, delta angle=290];
+\draw [thick] (\sqcx,\sqcy) arc[radius=0.1, start angle=-60, delta angle=360];
+%\node (squareLab) at (0.5,0.5)  {$o$};
+\end{tikzpicture}%
+}
+\newcommand{\rrhFw}{\raisebox{-0.333\height}{\SquareFw}\,}
+%%
+\newcommand{\RubikFw}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareFw\\
+\rrFw
+\end{minipage}%
+}
+\newcommand{\textRubikFw}{\rrFw\,\rrhFw}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Fwp}
+%
+%  \begin{macro}{\rrFwp}
+%  \begin{macro}{\SquareFwp}
+%  \begin{macro}{\rrhFwp}
+%  \begin{macro}{\RubikFwp}
+%  \begin{macro}{\textRubikFwp}
+%  These commands  all draw forms which denote the Fwp rotation.
+% \begin{macrocode}
+\newcommand{\rrFwp}{\textbf{\textsf{F\footnotesize{w}}$^\prime$}}
+%%
+\newcommand{\SquareFwp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, ->] (\scx, \scy) arc[radius=0.35, start angle=-60, delta angle=290];
+\draw [thick] (\sqcx,\sqcy) arc[radius=0.1, start angle=-60, delta angle=360];
+\end{tikzpicture}%
+}
+\newcommand{\rrhFwp}{\raisebox{-0.333\height}{\SquareFwp}\,}
+%%
+\newcommand{\RubikFwp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareFwp\\
+\rrFwp
+\end{minipage}%
+}
+\newcommand{\textRubikFwp}{\rrFwp\,\rrhFwp}
+%%
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Fs}
+%
+%  \begin{macro}{\rrFs}
+%  \begin{macro}{\rrhFs}
+%  \begin{macro}{\RubikFs}
+%  \begin{macro}{\textRubikFs}
+%  These commands  draw forms of the Singmaster Fs slice rotation.
+%  We need to just make square with Fs 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{\rrFs}{\@rrs{F}}
+\newcommand{\SquareFs}{\@SquareLetter{\rrFs}} 
+\newcommand{\rrhFs}{\raisebox{-0.25mm}{\SquareFs}\,}
+\newcommand{\RubikFs}{\raisebox{\@hRubik}{\SquareFs}\,}
+\newcommand{\textRubikFs}{\rrhFs\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Fsp}
+%
+%  \begin{macro}{\rrFsp}
+%  \begin{macro}{\rrhFsp}
+%  \begin{macro}{\RubikFsp}
+%  \begin{macro}{\textRubikFsp}
+%  These commands  draw forms of the Singmaster Fsp slice rotation.
+%  We need to just make square with Fsp 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{\rrFsp}{\@rrsp{F}}
+\newcommand{\SquareFsp}{\@SquareLetter{\rrFsp}}
+\newcommand{\rrhFsp}{\raisebox{-0.25mm}{\SquareFsp}\,}
+\newcommand{\RubikFsp}{\raisebox{\@hRubik}{\SquareFsp}\,}
+\newcommand{\textRubikFsp}{\rrhFsp\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Fa}
+%
+%  \begin{macro}{\rrFa}
+%  \begin{macro}{\rrhFa}
+%  \begin{macro}{\RubikFa}
+%  \begin{macro}{\textRubikFa}
+%  These commands  draw forms of the Singmaster Fa slice rotation.
+%  We need to just make square with Fa 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{\rrFa}{\@rra{F}}
+\newcommand{\SquareFa}{\@SquareLetter{\rrFa}}
+\newcommand{\rrhFa}{\raisebox{-0.25mm}{\SquareFa}\,}
+\newcommand{\RubikFa}{\raisebox{\@hRubik}{\SquareFa}\,}
+\newcommand{\textRubikFa}{\rrhFa\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Fap}
+%
+%  \begin{macro}{\rrFap}
+%  \begin{macro}{\rrhFap}
+%  \begin{macro}{\RubikFap}
+%  \begin{macro}{\textRubikFap}
+%  These commands  draw forms of the Singmaster Fap slice rotation.
+%  We need to just make square with Fap 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{\rrFap}{\@rrap{F}}
+\newcommand{\SquareFap}{\@SquareLetter{\rrFap}}
+\newcommand{\rrhFap}{\raisebox{-0.25mm}{\SquareFap}\,}
+\newcommand{\RubikFap}{\raisebox{\@hRubik}{\SquareFap}\,}
+\newcommand{\textRubikFap}{\rrhFap\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation L}
+%
+%  \begin{macro}{\rrL}
+%  \begin{macro}{\SquareL}
+%  \begin{macro}{\rrhL}
+%  \begin{macro}{\RubikL}
+%  \begin{macro}{\textRubikL}
+%  These commands  all draw forms which denote the L rotation.
+% \begin{macrocode}
+\newcommand{\rrL}{\textbf{\textsf{L}}}
+%%
+\newcommand{\SquareL}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, <-] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhL}{\raisebox{-0.333\height}{\SquareL}\,}
+%%
+\newcommand{\RubikL}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareL\\
+\rrL
+\end{minipage}%
+}
+\newcommand{\textRubikL}{\rrL\,\rrhL}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Lp}
+%
+%  \begin{macro}{\rrLp}
+%  \begin{macro}{\SquareLp}
+%  \begin{macro}{\rrhLp}
+%  \begin{macro}{\RubikLp}
+%  \begin{macro}{\textRubikLp}
+%  These commands  all draw forms which denote the Lp rotation.
+% \begin{macrocode}
+\newcommand{\rrLp}{\textbf{\textsf{L}$^\prime$}}
+%%
+\newcommand{\SquareLp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick,->] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhLp}{\raisebox{-0.333\height}{\SquareLp}\,}
+%%
+\newcommand{\RubikLp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareLp\\
+\rrLp
+\end{minipage}%
+}
+\newcommand{\textRubikLp}{\rrLp\,\rrhLp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Lw}
+%
+%  \begin{macro}{\rrLw}
+%  \begin{macro}{\SquareLw}
+%  \begin{macro}{\rrhLw}
+%  \begin{macro}{\RubikLw}
+%  \begin{macro}{\textRubikLw}
+%  These commands  all draw forms which denote the Lw rotation.
+% \begin{macrocode}
+\newcommand{\rrLw}{\textbf{\textsf{L\footnotesize{w}}}}
+%%
+\newcommand{\SquareLw}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, <-] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick, <-] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhLw}{\raisebox{-0.333\height}{\SquareLw}\,}
+%%
+\newcommand{\RubikLw}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareLw\\
+\rrLw
+\end{minipage}%
+}
+\newcommand{\textRubikLw}{\rrLw\,\rrhLw}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Lwp}
+%
+%  \begin{macro}{\rrLwp}
+%  \begin{macro}{\SquareLwp}
+%  \begin{macro}{\rrhLwp}
+%  \begin{macro}{\RubikLwp}
+%  \begin{macro}{\textRubikLwp}
+%  These commands  all draw forms which denote the Lwp rotation.
+% \begin{macrocode}
+\newcommand{\rrLwp}{\textbf{\textsf{L\footnotesize{w}}$^\prime$}}
+%%
+\newcommand{\SquareLwp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick,->] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick,->] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhLwp}{\raisebox{-0.333\height}{\SquareLwp}\,}
+%%
+\newcommand{\RubikLwp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareLwp\\
+\rrLwp
+\end{minipage}%
+}
+\newcommand{\textRubikLwp}{\rrLwp\,\rrhLwp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{    Rotation Ls}
+%
+%  \begin{macro}{\rrLs}
+%  \begin{macro}{\SquareLs}
+%  \begin{macro}{\rrhLs}
+%  \begin{macro}{\RubikLs}
+%  \begin{macro}{\textRubikLs}
+%  These commands  all draw forms which denote the Ls rotation.
+% \begin{macrocode}
+\newcommand{\rrLs}{\@rrs{L}}
+%%
+\newcommand{\SquareLs}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, <-] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick, <-] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhLs}{\raisebox{-0.333\height}{\SquareLs}\,}
+%%
+\newcommand{\RubikLs}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareLs\\
+\rrLs
+\end{minipage}%
+}
+\newcommand{\textRubikLs}{\rrLs\,\rrhLs}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{    Rotation Lsp}
+%
+%  \begin{macro}{\rrLsp}
+%  \begin{macro}{\SquareLsp}
+%  \begin{macro}{\rrhLsp}
+%  \begin{macro}{\RubikLsp}
+%  \begin{macro}{\textRubikLsp}
+%  These commands  all draw forms which denote the Lsp rotation.
+% \begin{macrocode}
+\newcommand{\rrLsp}{\@rrsp{L}}
+%%
+\newcommand{\SquareLsp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, ->] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick, ->] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhLsp}{\raisebox{-0.333\height}{\SquareLsp}\,}
+%%
+\newcommand{\RubikLsp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareLsp\\
+\rrLsp
+\end{minipage}%
+}
+\newcommand{\textRubikLsp}{\rrLsp\,\rrhLsp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{    Rotation La}
+%
+%  \begin{macro}{\rrLa}
+%  \begin{macro}{\SquareLa}
+%  \begin{macro}{\rrhLa}
+%  \begin{macro}{\RubikLa}
+%  \begin{macro}{\textRubikLa}
+%  These commands  all draw forms which denote the La rotation.
+% \begin{macrocode}
+\newcommand{\rrLa}{\@rra{L}}
+%%
+\newcommand{\SquareLa}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, <-] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick, ->] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhLa}{\raisebox{-0.333\height}{\SquareLa}\,}
+%%
+\newcommand{\RubikLa}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareLa\\
+\rrLa
+\end{minipage}%
+}
+\newcommand{\textRubikLa}{\rrLa\,\rrhLa}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Lap}
+%
+%  \begin{macro}{\rrLap}
+%  \begin{macro}{\SquareLap}
+%  \begin{macro}{\rrhLap}
+%  \begin{macro}{\RubikLap}
+%  \begin{macro}{\textRubikLap}
+%  These commands  all draw forms which denote the Lap rotation.
+% \begin{macrocode}
+\newcommand{\rrLap}{\@rrap{L}}
+%%
+\newcommand{\SquareLap}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, ->] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick, <-] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhLap}{\raisebox{-0.333\height}{\SquareLap}\,}
+%%
+\newcommand{\RubikLap}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareLap\\
+\rrLap
+\end{minipage}%
+}
+\newcommand{\textRubikLap}{\rrLap\,\rrhLap}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{    Rotation M}
+%
+%  \begin{macro}{\rrM}
+%  \begin{macro}{\SquareM}
+%  \begin{macro}{\rrhM}
+%  \begin{macro}{\RubikM}
+%  \begin{macro}{\textRubikM}
+%  These commands  all draw forms which denote the M rotation.
+% \begin{macrocode}
+\newcommand{\rrM}{\textbf{\textsf{M}}}
+%%
+\newcommand{\SquareM}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick, <-] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhM}{\raisebox{-0.333\height}{\SquareM}\,}
+%%
+\newcommand{\RubikM}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareM\\
+\rrM
+\end{minipage}%
+}
+\newcommand{\textRubikM}{\rrM\,\rrhM}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Mp}
+%
+%  \begin{macro}{\rrMp}
+%  \begin{macro}{\SquareMp}
+%  \begin{macro}{\rrhMp}
+%  \begin{macro}{\RubikMp}
+%  \begin{macro}{\textRubikMp}
+%  These commands  all draw forms which denote the Mp rotation.
+% \begin{macrocode}
+\newcommand{\rrMp}{\textbf{\textsf{M}$^\prime$}}
+%%
+\newcommand{\SquareMp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick,->] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhMp}{\raisebox{-0.333\height}{\SquareMp}\,}
+%%
+\newcommand{\RubikMp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareMp\\
+\rrMp
+\end{minipage}%
+}
+\newcommand{\textRubikMp}{\rrMp\,\rrhMp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{    Rotation R}
+%
+%  \begin{macro}{\rrR}
+%  \begin{macro}{\SquareR}
+%  \begin{macro}{\rrhR}
+%  \begin{macro}{\RubikR}
+%  \begin{macro}{\textRubikR}
+%  These commands  all draw forms which denote the R rotation.
+% \begin{macrocode}
+\newcommand{\rrR}{\textbf{\textsf{R}}}
+%%
+\newcommand{\SquareR}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+%% draw three lines in the square, one with an arrow
+\draw [thick] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick, ->] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhR}{\raisebox{-0.333\height}{\SquareR}\,}
+%%
+\newcommand{\RubikR}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareR\\
+\rrR
+\end{minipage}%
+}
+\newcommand{\textRubikR}{\rrR\,\rrhR}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{    Rotation Rp}
+%
+%  \begin{macro}{\rrRp}
+%  \begin{macro}{\SquareRp}
+%  \begin{macro}{\rrhRp}
+%  \begin{macro}{\RubikRp}
+%  \begin{macro}{\textRubikRp}
+%  These commands  all draw forms which denote the Rp rotation.
+% \begin{macrocode}
+\newcommand{\rrRp}{\textbf{\textsf{R}$^\prime$}}
+%%
+\newcommand{\SquareRp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick, <-] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhRp}{\raisebox{-0.333\height}{\SquareRp}\,}
+%%
+\newcommand{\RubikRp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareRp\\
+\rrRp
+\end{minipage}%
+}
+\newcommand{\textRubikRp}{\rrRp\,\rrhRp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{    Rotation Rw}
+%
+%  \begin{macro}{\rrRw}
+%  \begin{macro}{\SquareRw}
+%  \begin{macro}{\rrhRw}
+%  \begin{macro}{\RubikRw}
+%  \begin{macro}{\textRubikRw}
+%  These commands  all draw forms which denote the Rw rotation.
+% \begin{macrocode}
+\newcommand{\rrRw}{\textbf{\textsf{R\footnotesize{w}}}}
+%%
+\newcommand{\SquareRw}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick, ->] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick, ->] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhRw}{\raisebox{-0.333\height}{\SquareRw}\,}
+%%
+\newcommand{\RubikRw}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareRw\\
+\rrRw
+\end{minipage}%
+}
+\newcommand{\textRubikRw}{\rrRw\,\rrhRw}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{    Rotation Rwp}
+%
+%  \begin{macro}{\rrRwp}
+%  \begin{macro}{\SquareRwp}
+%  \begin{macro}{\rrhRwp}
+%  \begin{macro}{\RubikRwp}
+%  \begin{macro}{\textRubikRwp}
+%  These commands  all draw forms which denote the Rwp rotation.
+% \begin{macrocode}
+\newcommand{\rrRwp}{\textbf{\textsf{R\footnotesize{w}}$^\prime$}}
+%%
+\newcommand{\SquareRwp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick, <-] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick, <-] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhRwp}{\raisebox{-0.333\height}{\SquareRwp}\,}
+%%
+\newcommand{\RubikRwp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareRwp\\
+\rrRwp
+\end{minipage}%
+}
+\newcommand{\textRubikRwp}{\rrRwp\,\rrhRwp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Rs}
+%
+%  \begin{macro}{\rrRs}
+%  \begin{macro}{\SquareRs}
+%  \begin{macro}{\rrhRs}
+%  \begin{macro}{\RubikRs}
+%  \begin{macro}{\textRubikRs}
+%  These commands  all draw forms which denote the Rs rotation.
+% \begin{macrocode}
+\newcommand{\rrRs}{\@rrs{R}}
+%%
+\newcommand{\SquareRs}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick,->] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick,->] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhRs}{\raisebox{-0.333\height}{\SquareRs}\,}
+%%
+\newcommand{\RubikRs}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareRs\\
+\rrRs
+\end{minipage}%
+}
+\newcommand{\textRubikRs}{\rrRs\,\rrhRs}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Rsp}
+%
+%  \begin{macro}{\rrRsp}
+%  \begin{macro}{\SquareRsp}
+%  \begin{macro}{\rrhRsp}
+%  \begin{macro}{\RubikRsp}
+%  \begin{macro}{\textRubikRsp}
+%  These commands  all draw forms which denote the Rsp rotation.
+% \begin{macrocode}
+\newcommand{\rrRsp}{\@rrsp{R}}
+%%
+\newcommand{\SquareRsp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick,<-] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick,<-] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhRsp}{\raisebox{-0.333\height}{\SquareRsp}\,}
+%%
+\newcommand{\RubikRsp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareRsp\\
+\rrRsp
+\end{minipage}%
+}
+\newcommand{\textRubikRsp}{\rrRsp\,\rrhRsp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Ra}
+%
+%  \begin{macro}{\rrRa}
+%  \begin{macro}{\SquareRa}
+%  \begin{macro}{\rrhRa}
+%  \begin{macro}{\RubikRa}
+%  \begin{macro}{\textRubikRa}
+%  These commands  all draw forms which denote the Ra rotation.
+% \begin{macrocode}
+\newcommand{\rrRa}{\@rra{R}}
+%%
+\newcommand{\SquareRa}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick,<-] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick,->] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhRa}{\raisebox{-0.333\height}{\SquareRa}\,}
+%%
+\newcommand{\RubikRa}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareRa\\
+\rrRa
+\end{minipage}%
+}
+\newcommand{\textRubikRa}{\rrRa\,\rrhRa}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Rap}
+%
+%  \begin{macro}{\rrRap}
+%  \begin{macro}{\SquareRap}
+%  \begin{macro}{\rrhRap}
+%  \begin{macro}{\RubikRap}
+%  \begin{macro}{\textRubikRap}
+%  These commands  all draw forms which denote the Rap rotation.
+% \begin{macrocode}
+\newcommand{\rrRap}{\@rrap{R}}
+%%
+\newcommand{\SquareRap}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick,->] (\sd, \sb) -- (\sd, \sbh);
+\draw [thick] (\sdd,\sb) -- (\sdd, \sbh);
+\draw [thick,<-] (\sddd, \sb) -- (\sddd, \sbh);
+\end{tikzpicture}%
+}
+\newcommand{\rrhRap}{\raisebox{-0.333\height}{\SquareRap}\,}
+%%
+\newcommand{\RubikRap}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareRap\\
+\rrRap
+\end{minipage}%
+}
+\newcommand{\textRubikRap}{\rrRap\,\rrhRap}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation S}
+%
+%  \begin{macro}{\rrS}
+%  \begin{macro}{\SquareS}
+%  \begin{macro}{\rrhS}
+%  \begin{macro}{\RubikS}
+%  \begin{macro}{\textRubikS}
+%  These commands  all draw forms which denote the S rotation.
+% 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\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Sp}
+%
+%  \begin{macro}{\rrSp}
+%  \begin{macro}{\SquareSp}
+%  \begin{macro}{\rrhSp}
+%  \begin{macro}{\RubikSp}
+%  \begin{macro}{\textRubikSp}
+%  These commands  all draw forms which denote the Sp rotation.
+% 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\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Su}
+%
+%  \begin{macro}{\rrSu}
+%  \begin{macro}{\rrhSu}
+%  \begin{macro}{\RubikSu}
+%  \begin{macro}{\textRubikSu}
+%  These commands  draw forms of the Singmaster Su slice rotation.
+%  We also need to finetune the spacing 
+%  between these `slice' hieroglyphs (especially Fs  and Bs).
+% \begin{macrocode}
+\newcommand{\rrSu}{\textbf{\textsf{S\footnotesize{u}}}}
+\newcommand{\rrhSu}{\rrhEp}%
+\newcommand{\RubikSu}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareEp\\
+\rrSu
+\end{minipage}%
+}
+\newcommand{\textRubikSu}{\rrSu\,\rrhEp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Sup}
+%
+%  \begin{macro}{\rrSup}
+%  \begin{macro}{\rrhSup}
+%  \begin{macro}{\RubikSup}
+%  \begin{macro}{\textRubikSup}
+%  These commands  draw forms of the Singmaster Sup slice rotation.
+%  We also need to finetune the spacing 
+%  between these `slice' hieroglyphs (especially Fs  and Bs).
+% \begin{macrocode}
+\newcommand{\rrSup}{\textbf{\textsf{S\footnotesize{u}}$^\prime$}}
+\newcommand{\rrhSup}{\rrhE}%
+\newcommand{\RubikSup}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareE\\
+\rrSup
+\end{minipage}%
+}
+\newcommand{\textRubikSup}{\rrSup\,\rrhE}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Sd}
+%
+%  \begin{macro}{\rrSd}
+%  \begin{macro}{\rrhSd}
+%  \begin{macro}{\RubikSd}
+%  \begin{macro}{\textRubikSd}
+%  These commands  draw forms of the Singmaster Sd slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSd}{\textbf{\textsf{S\footnotesize{d}}}}
+\newcommand{\rrhSd}{\rrhE}%
+\newcommand{\RubikSd}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareE\\
+\rrSd
+\end{minipage}%
+}
+\newcommand{\textRubikSd}{\rrSd\,\rrhE}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Sdp}
+%
+%  \begin{macro}{\rrSdp}
+%  \begin{macro}{\rrhSdp}
+%  \begin{macro}{\RubikSdp}
+%  \begin{macro}{\textRubikSdp}
+%  These commands  draw forms of the Singmaster Sdp slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSdp}{\textbf{\textsf{S\footnotesize{d}}$^\prime$}}
+\newcommand{\rrhSdp}{\rrhEp}%
+\newcommand{\RubikSdp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareEp\\
+\rrSdp
+\end{minipage}%
+}
+\newcommand{\textRubikSdp}{\rrSdp\,\rrhEp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Sl}
+%
+%  \begin{macro}{\rrSl}
+%  \begin{macro}{\rrhSl}
+%  \begin{macro}{\RubikSl}
+%  \begin{macro}{\textRubikSl}
+%  These commands  draw forms of the Singmaster Sl slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSl}{\textbf{\textsf{S\footnotesize{l}}}}
+\newcommand{\rrhSl}{\rrhM}%
+\newcommand{\RubikSl}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareM\\
+\rrSl
+\end{minipage}%
+}
+\newcommand{\textRubikSl}{\rrSl\,\rrhM}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Slp}
+%
+%  \begin{macro}{\rrSlp}
+%  \begin{macro}{\rrhSlp}
+%  \begin{macro}{\RubikSlp}
+%  \begin{macro}{\textRubikSlp}
+%  These commands  draw forms of the Singmaster Slp slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSlp}{\textbf{\textsf{S\footnotesize{l}}$^\prime$}}
+\newcommand{\rrhSlp}{\rrhMp}%
+\newcommand{\RubikSlp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareMp\\
+\rrSlp
+\end{minipage}%
+}
+\newcommand{\textRubikSlp}{\rrSlp\,\rrhMp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Sr}
+%
+%  \begin{macro}{\rrSr}
+%  \begin{macro}{\rrhSr}
+%  \begin{macro}{\RubikSr}
+%  \begin{macro}{\textRubikSr}
+%  These commands  draw forms of the Singmaster Sr slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSr}{\textbf{\textsf{S\footnotesize{r}}}}
+\newcommand{\rrhSr}{\rrhMp}%
+\newcommand{\RubikSr}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareMp\\
+\rrSr
+\end{minipage}%
+}
+\newcommand{\textRubikSr}{\rrSr\,\rrhMp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Srp}
+%
+%  \begin{macro}{\rrSrp}
+%  \begin{macro}{\rrhSrp}
+%  \begin{macro}{\RubikSrp}
+%  \begin{macro}{\textRubikSrp}
+%  These commands  draw forms of the Singmaster Srp slice rotation.
+% \begin{macrocode}
+\newcommand{\rrSrp}{\textbf{\textsf{S\footnotesize{r}}$^\prime$}}
+\newcommand{\rrhSrp}{\rrhM}%
+\newcommand{\RubikSrp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareM\\
+\rrSrp
+\end{minipage}%
+}
+\newcommand{\textRubikSrp}{\rrSrp\,\rrhM}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Sf}
+%
+%  \begin{macro}{\rrSf}
+%  \begin{macro}{\rrhSf}
+%  \begin{macro}{\RubikSf}
+%  \begin{macro}{\textRubikSf}
+%  These commands  draw forms of the Singmaster Sf 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}{\textbf{\textsf{S\footnotesize{f}}}}
+\newcommand{\SquareSf}{\@SquareLetter{\rrSf}}
+\newcommand{\rrhSf}{\raisebox{-0.25mm}{\SquareSf}\,}
+\newcommand{\RubikSf}{\raisebox{\@hRubik}{\SquareSf}\,}
+\newcommand{\textRubikSf}{\rrhSf\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Sfp}
+%
+%  \begin{macro}{\rrSfp}
+%  \begin{macro}{\rrhSfp}
+%  \begin{macro}{\RubikSfp}
+%  \begin{macro}{\textRubikSfp}
+%  These commands  draw forms of the Singmaster Sfp 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}{\textbf{\textsf{S\footnotesize{f}}$^\prime$}}
+\newcommand{\SquareSfp}{\@SquareLetter{\rrSfp}}
+\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{     Rotation Sb}
+%
+%  \begin{macro}{\rrSb}
+%  \begin{macro}{\rrhSb}
+%  \begin{macro}{\RubikSb}
+%  \begin{macro}{\textRubikSb}
+%  These commands  draw forms of the Singmaster Sb 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}{\textbf{\textsf{S\footnotesize{b}}}}
+\newcommand{\SquareSb}{\@SquareLetter{\rrSb}}
+\newcommand{\rrhSb}{\raisebox{-0.25mm}{\SquareSb}\,}
+\newcommand{\RubikSb}{\raisebox{\@hRubik}{\SquareSb}\,}
+\newcommand{\textRubikSb}{\rrhSb\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Sbp}
+%
+%  \begin{macro}{\rrSbp}
+%  \begin{macro}{\rrhSbp}
+%  \begin{macro}{\RubikSbp}
+%  \begin{macro}{\textRubikSbp}
+%  These commands  draw forms of the Singmaster Sbp 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 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\,}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation U}
+%
+%  \begin{macro}{\rrU}
+%  \begin{macro}{\SquareU}
+%  \begin{macro}{\rrhU}
+%  \begin{macro}{\RubikU}
+%  \begin{macro}{\textRubikU}
+%  These commands  all draw forms which denote the U rotation.
+% \begin{macrocode}
+\newcommand{\rrU}{\textbf{\textsf{U}}}
+%%
+\newcommand{\SquareU}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, <-] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick]     (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhU}{\raisebox{-0.333\height}{\SquareU}\,}
+%%
+\newcommand{\RubikU}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareU\\
+\rrU
+\end{minipage}%%
+}
+\newcommand{\textRubikU}{\rrU\,\rrhU}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Uw}
+%
+%  \begin{macro}{\rrUw}
+%  \begin{macro}{\SquareUw}
+%  \begin{macro}{\rrhUw}
+%  \begin{macro}{\RubikUw}
+%  \begin{macro}{\textRubikUw}
+%  These commands  all draw forms which denote the Uw rotation.
+% \begin{macrocode}
+\newcommand{\rrUw}{\textbf{\textsf{U\footnotesize{w}}}}
+%%
+\newcommand{\SquareUw}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, <-] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick, <-] (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+%
+\newcommand{\rrhUw}{\raisebox{-0.333\height}{\SquareUw}\,}
+%%
+\newcommand{\RubikUw}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareUw\\
+\rrUw
+\end{minipage}%%
+}
+%%
+\newcommand{\textRubikUw}{\rrUw\,\rrhUw}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Up}
+%
+%  \begin{macro}{\rrUp}
+%  \begin{macro}{\SquareUp}
+%  \begin{macro}{\rrhUp}
+%  \begin{macro}{\RubikUp}
+%  \begin{macro}{\textRubikUp}
+%  These commands  all draw forms which denote the Up rotation.
+% \begin{macrocode}
+\newcommand{\rrUp}{\textbf{\textsf{U}$^\prime$}}
+%%
+\newcommand{\SquareUp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, ->] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick]     (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhUp}{\raisebox{-0.333\height}{\SquareUp}\,}
+%%
+\newcommand{\RubikUp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareUp\\
+\rrUp
+\end{minipage}%%
+}
+\newcommand{\textRubikUp}{\rrUp\,\rrhUp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Uwp}
+%
+%  \begin{macro}{\rrUwp}
+%  \begin{macro}{\SquareUwp}
+%  \begin{macro}{\rrhUwp}
+%  \begin{macro}{\RubikUwp}
+%  \begin{macro}{\textRubikUwp}
+%  These commands  all draw forms which denote the Uwp rotation.
+% \begin{macrocode}
+\newcommand{\rrUwp}{\textbf{\textsf{U\footnotesize{w}}$^\prime$}}
+%%
+\newcommand{\SquareUwp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, ->] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick, ->] (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhUwp}{\raisebox{-0.333\height}{\SquareUwp}\,}
+%%
+\newcommand{\RubikUwp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareUwp\\
+\rrUwp
+\end{minipage}%%
+}
+\newcommand{\textRubikUwp}{\rrUwp\,\rrhUwp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Us} 
+%
+%  \begin{macro}{\rrUs}
+%  \begin{macro}{\SquareUs}
+%  \begin{macro}{\rrhUs}
+%  \begin{macro}{\RubikUs}
+%  \begin{macro}{\textRubikUs}
+%  These commands  all draw forms which denote the Us rotation.
+% \begin{macrocode}
+\newcommand{\rrUs}{\@rrs{U}}
+%%
+\newcommand{\SquareUs}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, <-] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick]     (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick, <-]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhUs}{\raisebox{-0.333\height}{\SquareUs}\,}
+%%
+\newcommand{\RubikUs}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareUs\\
+\rrUs
+\end{minipage}%
+}
+\newcommand{\textRubikUs}{\rrUs\,\rrhUs}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Usp} 
+%
+%  \begin{macro}{\rrUsp}
+%  \begin{macro}{\SquareUsp}
+%  \begin{macro}{\rrhUs}
+%  \begin{macro}{\RubikUs}
+%  \begin{macro}{\textRubikUsp}
+%  These commands  all draw forms which denote the Usp rotation.
+% \begin{macrocode}
+\newcommand{\rrUsp}{\@rrsp{U}}
+%%
+\newcommand{\SquareUsp}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, ->] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick]     (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick, ->]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhUsp}{\raisebox{-0.333\height}{\SquareUsp}\,}
+%%
+\newcommand{\RubikUsp}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareUsp\\
+\rrUsp
+\end{minipage}%
+}
+\newcommand{\textRubikUsp}{\rrUsp\,\rrhUsp}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Ua} 
+%
+%  \begin{macro}{\rrUa}
+%  \begin{macro}{\SquareUa}
+%  \begin{macro}{\rrhUa}
+%  \begin{macro}{\RubikUa}
+%  \begin{macro}{\textRubikUa}
+%  These commands  all draw forms which denote the Ua rotation.
+% \begin{macrocode}
+\newcommand{\rrUa}{\@rra{U}}
+%%
+\newcommand{\SquareUa}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, <-] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick]     (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick, ->]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhUa}{\raisebox{-0.333\height}{\SquareUa}\,}
+%%
+\newcommand{\RubikUa}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareUa\\
+\rrUa
+\end{minipage}%
+}
+\newcommand{\textRubikUa}{\rrUa\,\rrhUa}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotation Uap} 
+%
+%  \begin{macro}{\rrUap}
+%  \begin{macro}{\SquareUap}
+%  \begin{macro}{\rrhUap}
+%  \begin{macro}{\RubikUap}
+%  \begin{macro}{\textRubikUap}
+%  These commands  all draw forms which denote the Uap rotation.
+% \begin{macrocode}
+\newcommand{\rrUap}{\@rrap{U}}
+%%
+\newcommand{\SquareUap}{%
+\begin{tikzpicture}[scale=0.5]
+\DrawNotationBox;
+\draw [thick, ->] (\sb,\sddd) -- (\sbh, \sddd);
+\draw [thick]     (\sb,\sdd) --  (\sbh, \sdd);
+\draw [thick, <-]     (\sb,\sd) --   (\sbh, \sd);
+\end{tikzpicture}%
+}
+\newcommand{\rrhUap}{\raisebox{-0.333\height}{\SquareUap}\,}
+%%
+\newcommand{\RubikUap}{%
+\begin{minipage}{0.6cm}
+\centering
+\SquareUap\\
+\rrUap
+\end{minipage}%
+}
+\newcommand{\textRubikUap}{\rrUap\,\rrhUap}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsection{    Rotation commands --- axis rotations}
+%
+%  \subsubsection{    Rotations x and xp}
+%
+%  \begin{macro}{\rrx}
+%  \begin{macro}{\rrhx}
+%  \begin{macro}{\Rubikx}
+%  These commands  all draw forms which denote the x rotation.
+% \begin{macrocode}
+\newcommand{\rrx}{\textbf{\textsf{x}}}
+\newcommand{\Rubikx}{\@xyzRubik{x}}
+\newcommand{\rrhx}{\@xyzh{x}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrxp}
+%  \begin{macro}{\rrhxp}
+%  \begin{macro}{\Rubikxp}
+%  These commands  all draw forms which denote the xp rotation.
+% \begin{macrocode}
+\newcommand{\rrxp}{\textbf{\textsf{x}$^\prime$}}
+\newcommand{\Rubikxp}{\@xyzRubikp{x}}
+\newcommand{\rrhxp}{\@xyzhp{x}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotations y and yp}
+%
+%  \begin{macro}{\rry}
+%  \begin{macro}{\rrhy}
+%  \begin{macro}{\Rubiky}
+%  These commands  all draw forms which denote the y rotation.
+% \begin{macrocode}
+\newcommand{\rry}{\textbf{\textsf{y}}}
+\newcommand{\Rubiky}{\@xyzRubik{y}}
+\newcommand{\rrhy}{\@xyzh{y}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rryp}
+%  \begin{macro}{\rrhyp}
+%  \begin{macro}{\Rubikyp}
+%  These commands  all draw forms which denote the yp rotation.
+% \begin{macrocode}
+\newcommand{\rryp}{\textbf{\textsf{y}$^\prime$}}
+\newcommand{\Rubikyp}{\@xyzRubikp{y}}
+\newcommand{\rrhyp}{\@xyzhp{y}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotations z and zp}
+%
+%  \begin{macro}{\rrz}
+%  \begin{macro}{\rrhz}
+%  \begin{macro}{\Rubikz}
+%  These commands  all draw forms which denote the z rotation.
+% \begin{macrocode}
+\newcommand{\rrz}{\textbf{\textsf{z}}}
+\newcommand{\Rubikz}{\@xyzRubik{z}}
+\newcommand{\rrhz}{\@xyzh{z}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrzp}
+%  \begin{macro}{\rrhzp}
+%  \begin{macro}{\Rubikzp}
+%  These commands  all draw forms which denote the zp rotation.
+% \begin{macrocode}
+\newcommand{\rrzp}{\textbf{\textsf{z}$^\prime$}}
+\newcommand{\Rubikzp}{\@xyzRubikp{z}}
+\newcommand{\rrhzp}{\@xyzhp{z}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotations u and d}
+%
+%  \begin{macro}{\rru}
+%  \begin{macro}{\rrhu}
+%  \begin{macro}{\Rubiku}
+%  These commands  all draw forms which denote the u rotation.
+% \begin{macrocode}
+\newcommand{\rru}{\textbf{\textsf{u}}}
+\newcommand{\Rubiku}{\@xyzRubik{u}}
+\newcommand{\rrhu}{\@xyzh{u}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrd}
+%  \begin{macro}{\rrhd}
+%  \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}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotations l and r}
+%
+%  \begin{macro}{\rrl}
+%  \begin{macro}{\rrhl}
+%  \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}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrr}
+%  \begin{macro}{\rrhr}
+%  \begin{macro}{\Rubikr}
+%  These commands  all draw forms which denote the r rotation.
+% \begin{macrocode}
+\newcommand{\rrr}{\textbf{\textsf{r}}}
+\newcommand{\Rubikr}{\@xyzRubik{r}}
+\newcommand{\rrhr}{\@xyzh{r}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \subsubsection{     Rotations f and b}
+%
+%  \begin{macro}{\rrf}
+%  \begin{macro}{\rrhf}
+%  \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}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%  \begin{macro}{\rrb}
+%  \begin{macro}{\rrhb}
+%  \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}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%
+% --------------------------
+%    End of this package
+% --------------------------
+%    \begin{macrocode}
+%</rubikcube>
+%    \end{macrocode}
+%
+%
+%
+%
+% \Finale
+%
+\endinput
diff --git a/Master/texmf-dist/source/latex/rubik/rubikcube.ins b/Master/texmf-dist/source/latex/rubik/rubikcube.ins
new file mode 100644
index 00000000000..5b5d6d5f45a
--- /dev/null
+++ b/Master/texmf-dist/source/latex/rubik/rubikcube.ins
@@ -0,0 +1,76 @@
+%% rubikcube.dtx
+%% Copyright 2014  RWD Nickalls (dick@nickalls.org) and A Syropoulos (asyropoulos@yahoo.com)
+%%
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%   http://www.latex-project.org/lppl.txt
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 2005/12/01 or later.
+%%
+%% This work has the LPPL maintenance status `maintained'.
+%% 
+%% The Current Maintainer of this work are  RWD Nickalls and A Syropoulos
+%%
+%%
+%% This work consists of the files rubikcube.dtx and rubikcube.ins
+%% and the derived file rubikcube.sty.
+%%
+%% --------------- start of docstrip commands ------------------
+%%
+\def\batchfile{rubikcube.ins}
+\input docstrip.tex
+
+\preamble
+
+----------------------------------------------------------------- 
+  Authors: RWD Nickalls (dick@nickalls.org) 
+          and Apostolos Syropoulos (asyropoulos@yahoo.com)
+
+  Copyright 2014  RWD Nickalls and A Syropoulos
+
+
+  This work may be distributed and/or modified under the
+  conditions of the LaTeX Project Public License, either
+  version 1.3 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{rubikcube.sty}{\from{rubikcube.dtx}{rubikcube}}}
+
+%%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{*       rubikcube.sty                                *}
+\Msg{*                                                     *}
+\Msg{* To produce the documentation run the file           *}
+\Msg{* rubikcube.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/rubikrotation.dtx b/Master/texmf-dist/source/latex/rubik/rubikrotation.dtx
new file mode 100644
index 00000000000..8ffc824499a
--- /dev/null
+++ b/Master/texmf-dist/source/latex/rubik/rubikrotation.dtx
@@ -0,0 +1,987 @@
+% \iffalse meta-comment
+% rubikrotation.dtx
+%
+% Authors: RWD Nickalls (dick@nickalls.org) 
+%        and Apostolos Syropoulos (asyropoulos@yahoo.com)
+
+% Copyright 2014  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 rubikrotation 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{rubikrotation.sty}{\usepackage{rubikrotation}}{%
+    \GenericWarning{rubikrotation.dtx}{Package file rubikrotation.sty not found.
+    Documentation will be messed up!^^J
+    (Generate rubikrotation.sty by (La)TeXing rubikrotation.ins, and then^^J
+    process rubikrotation.dtx again)^^J}\stop
+}%
+\usepackage{ifpdf}
+\usepackage{url}  %% for references
+\usepackage{graphicx} %% for the two pdf figs
+%%\OnlyDescription
+\EnableCrossrefs
+\CodelineIndex
+\CodelineNumbered
+\RecordChanges
+\setcounter{StandardModuleDepth}{1}
+\begin{document}
+  \DocInput{rubikrotation.dtx}
+  \PrintChanges
+  \PrintIndex
+\end{document}
+%</driver>
+% \fi
+%
+%
+% 
+% \CheckSum{302}
+%
+%%% \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{The \textsf{rubikrotation} package}
+%
+% \author{
+%      RWD Nickalls (dick@nickalls.org) \\
+%     A Syropoulos (asyropoulos@yahoo.com)
+%       }
+%  \date{This file describes version \RRfileversion, last revised \RRfiledate}
+%  \maketitle
+%
+%  \begin{abstract}
+%  The \rubikrotation\ package is an extension for  the 
+%   \textsf{rubikcube} package. It  provides  the \cmd{\RubikRotation} command which 
+%   processes on-the-fly  a sequence of Rubik rotation moves (using the Perl script
+%   \texttt{rubikrotation.pl}) and returns the new Rubik cube  state.  It  implements 
+%   some basic checking of the Rubik state, and also offers a command for  displaying
+%    any errors (\cmd{\ShowRubikErrors}).
+%   This package requires access to the \TeX\ \texttt{write18} facility by using the 
+%   \texttt{--shell-escape} commandline switch.
+%  The \textsf{rubikrotation} package has been road-tested  on a Microsoft 
+%  platform (with MikTeX and Strawberry Perl), on a Linux platform ({\TeX}Live and Mandriva),
+%  and on OpenIndiana (a Solaris platform).
+%  \end{abstract}
+%
+%
+% \bigskip
+%
+%  \tableofcontents
+%
+% \section{Introduction}
+%
+% The \rubikrotation\ package is a dynamic extension to the \textsc{rubikcube} package.
+% It consists of a style option (\texttt{rubikrotation.sty}) and a 
+%  Perl script  (\texttt{rubikrotation.pl}). 
+% 
+% The primary role of the \rubikrotation\ package is to  implement on-the-fly Rubik 
+% rotation sequences using the \cmd{\RubikRotation} command.  Consequently, this 
+% package requires  the use of the \texttt{--shell-escape} switch to allow 
+% commandline control of  the  Perl script, which is really the `engine' of this package.
+%  The \textsf{rubikrotation} package has been road-tested  on a Microsoft 
+%  platform (with 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.})
+%  and on a Linux platform ({\TeX}Live and Mandriva).
+%
+% The following  commands are made available  by  \texttt{rubikrotation.sty}.
+% \begin{quote}
+% \begin{verbatim}
+%    \RubikRotation{}
+%    \SaveRubikState
+%    \CheckRubikState
+%    \ShowRubikErrors
+%\end{verbatim}
+% \end{quote}
+% Note that if the Perl script is not located in  the local working directory,  then
+%  some care is needed regarding placing  it where your system can both find it and 
+% also run it. In this case, the setting up of a simple one or two-line  configuration 
+% file may be  useful or even necessary, depending on your system
+%  (see section on `installation' below).
+%
+%
+%  \section{Requirements}
+% 
+% The \rubikrotation\ package  requires the TikZ and the \textsc{rubikcube} packages.
+% 
+%
+%   \section{Installation}
+%
+%  \subsection{Generating the files}
+%
+%  Place the file \texttt{rubikrotation.zip} into a temporary directory, and unzip it. 
+% This will generate the following files:
+% \begin{verbatim}
+% rubikrotation.ins
+% rubikrotation.dtx
+% rubikrotation.sty
+% rubikrotation.pl
+% rubikrotation.PDF
+% example-rot1.tex
+% example-rot1.PDF
+% example-rot2.tex
+% example-rot2.PDF
+%\end{verbatim}
+%  The  style option \texttt{rubikrotation.sty} is generated by  running (pdf)\LaTeX\ on  
+% the file \texttt{rubikrotation.ins}  as follows:
+%\begin{verbatim}
+%   pdflatex  rubikrotation.ins 
+%\end{verbatim}
+% The documentation file (\texttt{rubikrotation.pdf}) was generated using the following
+% steps:
+% \begin{verbatim}
+%  pdflatex  --shell-escape  rubikrotation.dtx
+%  pdflatex  --shell-escape  rubikrotation.dtx
+%  makeindex -s gind.ist  rubikrotation
+%  makeindex -s gglo.ist -o rubikrotation.gls  rubikrotation.glo
+%  pdflatex  --shell-escape  rubikrotation.dtx
+%\end{verbatim}
+%
+
+%
+%  \subsection{Placing the files}
+% \label{sec:placingfiles}
+%
+% Place the files either in the local working directory, or where your system 
+% will find them. For a Linux system with a standard \TeX\ Directory Structure (TDS), then:
+%
+%\medskip
+%{\noindent}*.sty  $\rightarrow$ 
+%   \texttt{/usr/local/texlive/texmf-local/tex/latex/local/rubikrotation/}
+%{\newline}*.cfg   $\rightarrow$ 
+%   \texttt{/usr/local/texlive/texmf-local/tex/latex/local/rubikrotation/}
+%{\newline}*.pdf  $\rightarrow$  \texttt{/usr/local/texlive/texmf-local/doc/rubikrotation/}
+%{\newline}*.pl  $\rightarrow$  \texttt{/usr/local/bin/}
+%
+% \medskip
+% {\noindent}Finally, (depending on your system) update the  \TeX\ file database using the 
+% \texttt{texhash} command.
+
+%
+%   \subsection{Configuration file}
+%   \label{sec:configfile}
+%
+%  A plane text configuration file with the name \texttt{rubikrotation.cfg} (if one exists)
+%  will be  read by the system. Such a file allows the user to 
+%  adjust (a)~the filename of the Perl script (\texttt{rubikrotation.pl}) 
+%  and (b)~the commandline code used by \texttt{rubikrotation.sty} for calling the 
+%  Perl script.  This sort of fine-tuning is sometimes convenient, and even necessary 
+%  (depending on your system), for locating and running the Perl script.
+%  For example, on some systems it maybe preferable  to use a different \textsc{path}, 
+%  file name and/or  a different  commandline code to  call the script.
+%
+%
+%  \DescribeMacro{\rubikperlname}
+%  \DescribeMacro{\rubikperlcmd}
+% The configuration file is essentially a convenient software vehicle for feeding some 
+% additional  \LaTeX\ code  to the  style option, and hence allow the contents of some 
+% commands to be 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 commandline call, 
+% namely  \cmd{\rubikperlcmd}.
+% The default definitions  for these (detailed in Section~\ref{sec:usefulcommands}) 
+% are as follows:
+%\begin{verbatim}
+% \newcommand{\rubikperlname}{rubikrotation.pl}
+% \newcommand{\rubikperlcmd}{perl \rubikperlname}
+%\end{verbatim}
+%
+%
+% For example, we might  wish to test out a slightly modified  Perl script, say
+% with the name \texttt{rubikrotationV3.pl}. In this case we simply  create,
+% in the local working directory, a plane text configuration file 
+% (called \texttt{rubikrotation.cfg})  which includes  the following line:
+%\begin{verbatim}
+%\renewcommand{\rubikperlname}{rubikrotationV3.pl}
+%\end{verbatim}
+%
+% Alternatively, say, if  the Perl script is being installed on a Linux platform,  then 
+% it would be standard to install it in the directory \texttt{/usr/local/bin}. 
+% A convenient approach in this case, therefore, would be to indicate this new \textsc{path} 
+% by including the following line in the configuration file:
+%\begin{verbatim}
+%\renewcommand{\rubikperlname}{/usr/local/bin/rubikrotation.pl}
+%\end{verbatim}
+% and, since this would then be an essentially permanent feature,  we would  then 
+% place the configuration file with the style option in the  
+%  \texttt{texmf-local/...} directory as described in section~\ref{sec:placingfiles} 
+% (placing files).  Note that in this case, we have \textit{not} made the Perl script 
+% `executable', since  the default commandline code is effectively 
+%  \texttt{perl  \rubikperlname}, and this  works  just as it is.
+%
+% However, if the Perl script \textit{is} made `executable', then 
+% a different commandline code will have to be used instead.
+% For example, suppose the Perl script is made  executable and  renamed to just  
+% \texttt{rubikrotation} (ie with no filename extension), then we  now have to 
+% omit the `perl' from the  default commandline. Consequently, we now need to make 
+% two command changes, which we implement  by  including the following 
+% two lines in the configuration file:
+%\begin{verbatim}
+%\renewcommand{\rubikperlname}{/usr/local/bin/rubikrotation}
+%\renewcommand{\rubikperlcmd}{\rubikperlname}
+%\end{verbatim}
+%
+%
+%       \section{Usage}
+%
+% Load the  packages \texttt{rubikcube.sty} 
+% and \texttt{rubikrotation.sty} in the \TeX\ file  \textit{after} loading 
+% the TikZ package, as follows: 
+%  \begin{verbatim}
+%  \usepackage{tikz}
+%  \usepackage{rubikcube,rubikrotation}
+%\end{verbatim}
+% and run (pdf)\LaTeX\ using the \texttt{--shell-escape} commandline switch 
+% (see following section).
+%
+%
+%   \subsection{Enabling the \TeX\ `shell' facility}
+%
+%  In order to enable the  \TeX\  `write18' facility (so it can run the Perl script) 
+% we will need to invoke (pdf)\LaTeX\ using the \texttt{--shell-escape} switch; say, as follows.
+% \begin{verbatim}
+% pdflatex  --shell-escape   filename.tex
+%\end{verbatim}
+% In practice, it is probably most convenient to  run this via a 
+% bash/batch file---something like the following, both of which 
+% automatically show the graphic output:
+% \begin{verbatim}
+% pdflatex  --shell-escape   filename.tex
+% xpdf filename.pdf
+%\end{verbatim}
+% or
+% \begin{verbatim}
+% latex  --shell-escape   filename.tex
+% dvips filename.dvi
+% gv filename.ps
+%\end{verbatim}
+%
+%
+%   \subsection{Test files}
+%
+% Two example  tex files (which demonstrate the use of the package commands) are 
+% included in the package, namely:
+% \begin{verbatim}
+% example-rot1.tex   (shows 5 worked examples)
+% example-rot2.tex   (is a `test' file for experimenting with different commands)
+%\end{verbatim}
+% These need to be run using  \texttt{--shell-escape} switch; for example:
+% \begin{verbatim}
+%  pdflatex  --shell-escape  example-rot1.tex
+%\end{verbatim}
+% If the files give unexpected results, check-out the log file to see if the system
+% has had any difficulties finding files etc.
+%
+%
+%
+%   \section{Commands}
+%
+%  The \textit{only} commands which \textit{must} be used inside a TikZ picture 
+%  environment are the \cmd{\Draw...} commands (these are all provided by 
+%  the \textsc{rubikcube} package), although most  commands  can be placed
+%  inside a TikZ environment if necessary. However, using commands outside the environment
+%  generally  offers maximum  flexibility, since the effects of commands used inside 
+%  a TikZ picture environment are `local' to  that picture environment, and are not 
+%  therefore accessable  outside the environment. 
+%
+%  The only command which must \textit{not}
+%  be inside a TikZ environment is the \cmd{\ShowRubikErrors} command 
+%  (see the notes on this command below). 
+% 
+%
+%   \subsection{\cmd{\RubikRotation} command}
+%
+%  \DescribeMacro{\RubikRotation}
+% The  \cmd{\RubikRotation}\marg{comma separated sequence}  command processes
+%  a comma separated sequence of rotations, and returns the final state.
+% 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. 
+% \begin{verbatim}
+% \begin{tikzpicture}[scale=0.7]
+%    \RubikCubeSolved
+%    \RubikRotation{R2,L,U,D}
+%    \DrawRubikCubeRU
+% \end{tikzpicture}
+%\end{verbatim}
+%  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 program \texttt{rubikrotation.pl}. The Perl 
+% program 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 and used to generate  
+% some graphic image of the cube. 
+%
+% Note that the \cmd{\RubikRotation} command can be either inside 
+% or before the Tikz picture environment. In fact only the `\cmd{\Draw...}' 
+% commands (from the \textsc{rubikcube} package) actually need to be inside
+% a TikZ picture environment. Consequently this makes for great flexibility. 
+%
+%  \subsubsection{Arguments prefixed with a *}
+%
+%  If any of the comma separated arguments (strings) is prefixed with a * it is 
+% not processed as a rotation. This feature therefore allows a string argument 
+% to be used as a label, which can be very useful.
+%  For example, we can use the * feature to label the following 
+% sequence as generating the so-called 
+% `sixspot' configuration (described by Reid):
+% \begin{verbatim}
+% \RubikRotation{*sixspot,U,Dp,R,Lp,F,Bp,U,Dp}
+%\end{verbatim}
+% Alternatively, and probably more conveniently, we could simply  use 
+% the name `sixspot' to define a new command, as follows (which therefore allows 
+% one to store lots of different rotation sequences by name alone):
+% \begin{verbatim}
+% \newcommand{\sixspot}{U,Dp,R,Lp,F,Bp,U,Dp}
+%\end{verbatim}
+% With this `newcommand' we are now able to generate the graphic (sixspot cube) 
+% much more easily using the following code:
+%
+% \medskip
+%
+% \begin{minipage}{6cm}
+% \begin{verbatim}
+% \begin{tikzpicture}[scale=0.7]
+%    \RubikCubeSolved
+%    \RubikRotation{\sixspot}
+%    \DrawRubikCubeRU
+% \end{tikzpicture}
+%\end{verbatim}
+% \end{minipage}
+% \begin{minipage}{3.4cm}
+% \centering
+% \ifpdf
+%   \includegraphics[height=3cm]{Rubikrot_doc_figA.pdf}
+% \else
+% \fi
+% \end{minipage}
+%
+%
+% \medskip
+%
+% In practice, it is quite useful to go one step further and  include 
+% the \texttt{*} label feature as well in the newcommand, as follows:
+% \begin{verbatim}
+% \newcommand{\sixspot}{*sixspot,U,Dp,R,Lp,F,Bp,U,Dp}
+%\end{verbatim}
+% since this has the great  advantage of making the particular 
+% rotation sequence identified by the label-name visible in the log file.
+% For example, the following command, which uses the rotations \textbf{x2} 
+% and \textbf{y} to  initially rotate the `solved' cube before applying 
+% the `sixspot' sequence  of rotations,
+% \begin{verbatim}
+% \RubikRotation{x2,y,\sixspot}
+%\end{verbatim}
+% will then be represented in the log file as 
+% \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 Bp U Dp (n= 11)
+% ...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 
+%\end{verbatim}
+% In this way, several named rotation sequences can be easily distinguished
+% in the log file from  adjacent  rotation commands.
+%
+%
+%   \subsubsection{Random rotations}
+%
+%  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 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 value $n=200$ will be used.
+% 
+% For example, the following commands will scramble a solved cube using a 
+% sequence of 120 random rotations, and display the state in the form of 
+%  a  semi-flat cube. 
+%
+%  \medskip
+%
+% \begin{minipage}{5.5cm}
+%\begin{verbatim}
+% \RubikCubeSolved%
+% \RubikRotation{random,120}%
+% \begin{tikzpicture}[scale=0.5]
+%    \DrawRubikCubeFlat
+% \end{tikzpicture}
+%\end{verbatim}
+% \end{minipage}
+% \begin{minipage}{3.4cm}
+% \centering
+% \ifpdf
+%   \includegraphics[height=4cm]{Rubikrot_doc_figB.pdf}
+% \else
+% \fi
+% \end{minipage}
+%
+% Note that in this particular example (above), only 
+% the \cmd{\Draw..} command is inside the TikZ picture environment---a useful
+% method when more than one figure is being drawn. Note also, that when such
+% commands are outside a TikZ picture environment, they should have a 
+% trailing \% to stop additional white space being included.
+%
+% \medskip
+%
+% The procedure is that all the possible rotations  are first allocated 
+% a different number (integer) and collected into an  array. Then  a 
+% sequence of $n$ randomised numbers is generated and  mapped to the array
+% to generate the associated sequence of random rotations. 
+% The sequence used is detailed in the \texttt{.log} file.
+%
+%
+%  \subsection{\cmd{\SaveRubikState}}
+%
+%  \DescribeMacro{\SaveRubikState}
+%  The command  \cmd{\SaveRubikState}\marg{filename} saves the state (configuration) 
+%  of the Rubik cube to  the file  \marg{filename} in the standard \cmd{\RubikFace...}
+%  format. Consequently such a file can then be input at a later stage so it can be
+%  drawn or processed in the usual way (inside the TikZ picture environment). 
+%
+% For example, the following commands would save the so-called `sixspot' configuration
+%  (generated by the rotations \textbf{U, Dp, R, Lp, F, Bp, U, Dp})
+% to the file \verb!sixspot.tex!.
+%\begin{verbatim}
+% \RubikCubeSolved%
+% \RubikRotation{*sixspot,U,Dp,R,Lp,F,Bp,U,Dp}%
+% \SaveRubikState{sixspot.tex}%
+%\end{verbatim}
+% The form of the  file \verb!sixspot.tex! will then be as follows---the 
+% filename (commented out) is automatically written to the  top of the 
+% file for convenience.
+%\begin{verbatim}
+% % filename: sixspot.tex
+% \RubikFaceUp{O}{O}{O}{O}{W}{O}{O}{O}{O}%
+% \RubikFaceDown{R}{R}{R}{R}{Y}{R}{R}{R}{R}%
+% \RubikFaceLeft{Y}{Y}{Y}{Y}{B}{Y}{Y}{Y}{Y}%
+% \RubikFaceRight{W}{W}{W}{W}{G}{W}{W}{W}{W}%
+% \RubikFaceFront{G}{G}{G}{G}{O}{G}{G}{G}{G}%
+% \RubikFaceBack{B}{B}{B}{B}{R}{B}{B}{B}{B}%
+%\end{verbatim}
+% We can therefore access and draw this configuration later, when required, 
+% simply by inputting  the file as follows:
+%\begin{verbatim}
+%\begin{tikzpicture}
+%    \input{sixspot.tex} 
+%    \DrawRubikCubeFlat
+%\end{tikzpicture}
+%\end{verbatim}
+%
+%
+%  \subsection{\cmd{\CheckRubikState} command}
+%
+%  \DescribeMacro{\CheckRubikState}
+%  Since it is easy to inadvertently define an invalid Rubik cube 
+% (eg enter an invalid number of, say, yellow cubies), this command 
+%  checks the current colour state of all the cubies
+% of a 3x3x3 Rubik cube, and  shows the number of cubies  of each colour.  
+% An ERROR: code is issued if the number of cubies having a given colour exceeds 6.
+% The results are written to the the \texttt{.log} file, and displayed under 
+% the graphic if the \cmd{\ShowRubikErrors} command is used.
+%
+% One can check the current Rubik state (for errors) by issuing  the command
+%\begin{verbatim}
+% \CheckRubikState%
+%\end{verbatim}
+% Note that  such a check is implemented automatically with each \cmd{\RubikRotation} command.
+%
+%
+%
+%
+%   \subsection{\cmd{\ShowRubikErrors} command}
+%
+%   \DescribeMacro{\ShowRubikErrors}
+%
+% Any errors which arise  can be made visible using  the 
+% command  \cmd{\ShowRubikErrors}. 
+% This command  places a copy of the `error' file (\texttt{rubikstateERRORS.dat})  
+% underneath the image so you can see any errors if there are any---all this 
+% detail can also be found in the \texttt{.log} file. 
+%
+%  Consequently, this  command must be placed \textit{after} a TikZ picture 
+%  environment---it cannot be used  inside a TikZ environment. In fact this command 
+%  is probably best placed at the  end of the document (if there are several such 
+%  environments), where it will reveal  all rotation errors  generated while 
+%  processing the document. 
+%
+%
+%    \section{Files generated}
+%
+% 
+% Whenever the \cmd{\RubikRotation} or \cmd{\CheckRubikState} commands are used, 
+% three small temporary  plain text files for holding data are generated  as 
+% follows (they are refreshed with each \LaTeX\ run, and are not actively deleted).
+% \begin{itemize}
+% \item  \LaTeX\ writes Rubik state data to the file \texttt{rubikstate.dat}.
+%
+% \item  Perl reads the file \texttt{rubikstate.dat} and then   writes 
+%  the new rubik state to the file \texttt{rubikstateNEW.dat}.
+%
+% \item   Perl also writes error data to the file \texttt{rubikstateERRORS.dat}. 
+%  A copy of this file is  displayed under the image  when the command 
+% \cmd{\ShowRubikErrors} is used after (outside) the TikZ picture environment.
+%
+% \end{itemize}
+%
+% 
+%     \section{General overview}
+%
+% When \LaTeX\  loads the \rubikrotation\ package  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}).
+% 
+% \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[4.]  The plain text file \texttt{rubikstateERRORS.dat} is created. 
+% This file collects error  messages generated by the Perl script.
+%
+% \end{itemize}
+%
+%
+% 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}). 
+% 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{U,D,L,R}! then the associated 
+%  \texttt{rubikstate.dat} file  would be as follows:
+% \begin{verbatim}
+% % filename: rubikstate.dat
+% up,W,W,W,W,W,W,W,W,W
+% down,Y,Y,Y,Y,Y,Y,Y,Y,Y
+% left,B,B,B,B,B,B,B,B,B
+% right,G,G,G,G,G,G,G,G,G
+% front,O,O,O,O,O,O,O,O,O
+% back,R,R,R,R,R,R,R,R,R
+% checkstate
+% rotation,U,D,L,R
+%\end{verbatim}
+% Alternatively, if the \cmd{\RubikRotation} command was 
+% \verb!\RubikRotation{random, 45}! then the last line  written to the file 
+% would be the string  `\texttt{rotation,random,45}' 
+% A  \cmd{\CheckRubikState} command   triggers the same sequence of events except
+% no `rotation' line is written.
+%
+% The action of the Perl program 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 Perl  program starts by loading the 
+% rubikstate (prompted by the keywords up, down, 
+%  left, right, front, back).  Next the program performs  
+% some basic checks (prompted by the key word `checkstate'), and then it processes 
+% the sequence of Rubik rotations (prompted by the keyword `rotation').
+% If, instead, the second argument  of the `rotation' string is the keyword `random', and
+% provided this is followed by a valid integer, say $n$, then the Perl program performs
+%  a sequence of $n$ random rotations.
+% Finally, the Perl program 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. 
+%
+% 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 `\texttt{Draw...}' command 
+% of some form is  reached 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
+% immediately under the graphic. Once the graphic is error-free, then the
+% \cmd{\ShowRubikErrors} can be removed or commented out. 
+%
+%
+%
+% ^^A ==================================================
+% \StopEventually{\PrintIndex}
+%
+%
+%
+%        \section{The code (\texttt{rubikrotation.sty})} 
+%  
+%   \subsection{Package heading}
+%
+%    \begin{macrocode}
+%<*rubikrotation>
+\def\RRfileversion{2.0}%
+\def\RRfiledate{2014/01/20}%
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{rubikrotation}[\RRfiledate\space (v\RRfileversion)]
+%    \end{macrocode}
+%
+%
+%  {\noindent}The package requires rubikcube.sty. Do not automatically
+% load rubikcube.sty since this makes it difficult to errorcheck new
+% versions (for the moment at least).
+%    \begin{macrocode}
+\@ifpackageloaded{rubikcube}{}{%
+   \typeout{---rubikrotation requires the rubikcube package.}%
+   }%
+%    \end{macrocode}
+%
+%
+%
+%  {\noindent}The \rubikrotation\  package requires access to the  fancyvrb package
+% for the \cmd{\VerbatimInput\{\}} command  which we use for inputting and displaying
+%   the error file.
+%    \begin{macrocode}
+\@ifpackageloaded{fancyvrb}{}{%
+   \typeout{---rubikrotation requires the fancyvrb package%
+       for VerbatimInput{} command.}%
+   \RequirePackage{fancyvrb}}
+%    \end{macrocode}
+%  \medskip
+%
+% 
+%\subsection{Some useful commands}
+% \label{sec:usefulcommands}
+%    \begin{macro}{\rubikrotation}
+% First we create a suitable logo
+%    \begin{macrocode}
+\newcommand{\rubikrotation}{\textsf{rubikrotation}}
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+%
+%    \begin{macro}{\@comment}
+%    \begin{macro}{\@commentone}
+%  We require  access to the percent character so we can write comments
+%  in files, including the log file.
+%  We first define percentchar for the write statement
+%  (From  Abrahams PW, Berry K and Hargreaves KA (1990), ``TeX for the Impatient'', p~292;
+%    available from: CTAN.../info/impatient/)
+%    \begin{macrocode}
+{\catcode`\%=12   \global\def\rubikpercentchar{%}}%
+\newcommand{\@comment}{\rubikpercentchar\rubikpercentchar\space}%
+\newcommand{\@commentone}{\rubikpercentchar}%
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%    \begin{macro}{\@print}
+%% We need  a simple print command for writing comments to a file.
+%    \begin{macrocode}
+\newcommand{\@print}[1]{\immediate\write\outfile{#1}}
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+%
+%    \begin{macro}{\rubikperlname}
+%  This holds the name of the Perl-5 script . It is used later to check
+%  whether the Perl script  exists or not. A plain text configuration file
+% \verb!rubikrotation.cfg! can be used to change the default name of the 
+% Perl script using a renewcommand. 
+%    \begin{macrocode}
+\newcommand{\rubikperlname}{rubikrotation.pl}
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+%    \begin{macro}{\rubikperlcmd}
+%  This holds the commandline  code for calling the the Perl script.
+%  A plain text  configuration file \verb!rubikrotation.cfg! can be used to 
+%  change the default commandline code  using a renewcommand. 
+%    \begin{macrocode}
+\newcommand{\rubikperlcmd}{perl \rubikperlname}
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+%\subsection{Configuration file}
+% If a config file exists (rubikrotation.cfg) then input it here,
+% ie \textit{after} defining the \cmd{\rubikperlname} and \cmd{\rubikperlcmd} 
+% commands and \textit{before} creating the \texttt{rubikstateERRORS.dat} file.
+%    \begin{macrocode}
+\typeout{---checking for config file (rubikrotation.cfg)...}
+\IfFileExists{rubikrotation.cfg}{%
+   \input{rubikrotation.cfg}%
+   }{\typeout{---no config file available}%
+}%
+%    \end{macrocode}
+%
+%
+%   \subsection{Clean file rubikstateNEW.dat}
+%
+% {\noindent}We need to clean any existing (old) rubikstateNEW.dat file,
+% since if the TeX shell switch is accidentally not used then  Perl will 
+% not be CALLed  and hence this file will not be renewed 
+% (ie an `old' image may be used).
+%    \begin{macrocode}
+\typeout{---cleaning file rubikstateNEW.dat}%
+\newwrite\outfile%
+\immediate\openout\outfile=rubikstateNEW.dat%
+\@print{\@comment rubikstateNEW.dat (by TeX)}%
+\immediate\closeout\outfile%
+%    \end{macrocode}
+%
+%
+%   \subsection{rubikstateERRORS.dat}
+%
+%  {\noindent}The \rubikrotation\  package requires the Perl program.
+% We first  open the file \texttt{rubikstateERRORS.dat} which is used
+% by the Perl program (\texttt{rubikrotation.pl}) for writing its error 
+% messages to.  This file is accessed and displayed by the command 
+% \cmd{\ShowRubikErrors}.
+%
+%  \textsc{important note}: this file is created fresh each time LaTeX is run
+%  and hence the Perl  program  only appends data to it during the \LaTeX\ run,
+%  so this file just grows until either it is  destroyed or recreated---a useful 
+%  feature to keep since the file  accumulates all error messages as the 
+% .tex file is processed.
+%  We can't make the Perl  program  create the file  since the Perl program is only 
+% CALLed if we  use a  \cmd{\RubikRotation} or \cmd{\CheckRubikState} 
+% command (which we may not!)---so it  has to be created (opened) here.
+%
+% The following code first opens the file, and then checks to see if 
+% the Perl program (\cmd{\rubikperlname}) exists; 
+% if the Perl prog does exist then all is OK, 
+% otherwise we write an error message to the file.
+%    \begin{macrocode}
+\typeout{---creating file rubikstateERRORS.dat}%
+\newwrite\outfile%
+\immediate\openout\outfile=rubikstateERRORS.dat%
+\@print{\@comment rubikstateERRORS.dat}%
+\typeout{---checking for Perl script \rubikperlname...}
+   \IfFileExists{\rubikperlname}{%
+   \typeout{---\rubikperlname\space exists OK}%
+   }{\typeout{** ERROR: cannot find Perl program \rubikperlname}%
+    \@print{\@comment ** ERROR: cannot find Perl program \rubikperlname}}%
+\immediate\closeout\outfile%
+%    \end{macrocode}
+%
+%
+%    \subsection{Setting up a newwrite  and file-access for new files}
+% 
+%  Having set up all the primary files, we now need to set up  a newwrite for 
+% all subsequent files openings (eg for rubikstate.dat and  saving 
+% to arbitrary filenames by the \cmd{\SaveRubikState} command). Otherwise, we 
+% can easily exceed the LaTeX limit of 15. From here-on  \TeX\ will use openout7
+% when opening and writing to files. We will implement new openings using
+% the command \verb!\@openstatefile! (see below). 
+%    \begin{macrocode}
+\typeout{---setting up newwrite for rubikrotation to use...}%
+\newwrite\outfile%
+%    \end{macrocode}
+%
+%
+%    \begin{macro}{\@openstatefile}
+%    \begin{macro}{\@closestatefile}
+% We also need   commands for easy file opening and  and closing
+% for new instances of the file \texttt{rubikstate.dat} etc.
+% Note that for this we are therefore using the same outfile number as set up
+% by the \verb!\newwrite...!  above. 
+%    \begin{macrocode}
+\newcommand{\@openstatefile}{\immediate\openout\outfile=rubikstate.dat}
+\newcommand{\@closestatefile}{\immediate\closeout\outfile}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%    \subsection{Saving the Rubik state}
+%
+%    \begin{macro}{\@printrubikstate}
+% This command  writes the Rubik configuration (state) to
+% the file \texttt{rubikstate.dat}, and is used by the \cmd{\RubikRotation} command.
+%  The file \texttt{rubikstate.dat} is read by the Perl program, and represents 
+% the state on which  the new \cmd{\RubikRotation} command acts.
+% Note that we append the key-word \texttt{checkstate} to the end of the file
+% in order to trigger the Perl program to implement its \texttt{checkstate} subroutine.
+%    \begin{macrocode}
+\newcommand{\@printrubikstate}{%
+   \@print{up,\Ult,\Umt,\Urt,\Ulm,\Umm,\Urm,\Ulb,\Umb,\Urb}%
+   \@print{down,\Dlt,\Dmt,\Drt,\Dlm,\Dmm,\Drm,\Dlb,\Dmb,\Drb}%
+   \@print{left,\Llt,\Lmt,\Lrt,\Llm,\Lmm,\Lrm,\Llb,\Lmb,\Lrb}%
+   \@print{right,\Rlt,\Rmt,\Rrt,\Rlm,\Rmm,\Rrm,\Rlb,\Rmb,\Rrb}%
+   \@print{front,\Flt,\Fmt,\Frt,\Flm,\Fmm,\Frm,\Flb,\Fmb,\Frb}%
+   \@print{back,\Blt,\Bmt,\Brt,\Blm,\Bmm,\Brm,\Blb,\Bmb,\Brb}%
+   \@print{checkstate}%
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+%    \subsection{RubikRotation command}
+%
+%    \begin{macro}{\RubikRotation}
+% The \cmd{\RubikRotation}\marg{comma separated sequence} 
+% command (a)~writes the current Rubik state to the file 
+% \texttt{rubikstate.dat}, and then (b)~CALLs the Perl program.
+% It also writes comments to the data file and also to the  log file.
+%    \begin{macrocode}
+\newcommand{\RubikRotation}[1]{\IfFileExists{\rubikperlname}{%
+   \typeout{---NEW rotation command------------------}%
+   \typeout{---command = RubikRotation{#1}}%
+   \typeout{---Perl script \rubikperlname\space exists OK}%
+   \typeout{---writing current Rubik state to file rubikstate.dat}%
+   \@openstatefile% open data file
+   \@print{\@comment filename: rubikstate.dat}%
+   \@printrubikstate% 
+   \@print{rotation,#1}%
+   \@closestatefile% close data file
+   \typeout{---running Perl script}%
+   \immediate\write18{\rubikperlcmd}%
+   \typeout{---inputting NEW datafile (from Perl)}%
+   \input{rubikstateNEW.dat}%
+   \typeout{-----------------------------------------}%
+ }{\typeout{** ERROR: \rubikperlname\space does not exist}%
+}}
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+%   \subsection{ShowRubikErrors command}
+%
+%    \begin{macro}{\ShowRubikErrors}
+% This command inputs the file \texttt{rubikstateERRORS.dat}.
+%    \begin{macrocode}
+\newcommand{\ShowRubikErrors}{%
+   \typeout{---ShowRubikErrors: inputting file rubikstateERRORS.dat}%
+   \VerbatimInput{rubikstateERRORS.dat}}
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+%   \subsection{CheckRubikState command}
+%
+%    \begin{macro}{\CheckRubikState}
+% This command triggers the Perl program to implement 
+%  some simple error checking of the Rubik configuration (state).
+% This command (a)~writes the current Rubik state to the file 
+% \texttt{rubikstate.dat}, and then (b)~CALLs the Perl program.
+% It also writes comments to the data file and also to the  log file..
+%    \begin{macrocode}
+\newcommand{\CheckRubikState}{\IfFileExists{\rubikperlname}{%
+   \typeout{---NEW check command------------------}%
+   \typeout{---command = CheckRubikState}%
+   \typeout{---Perl script \rubikperlname\space exists OK}%
+   \typeout{---writing current Rubik state to file rubikstate.dat}%
+   \@openstatefile% opens data file
+   \@print{\@comment filename: rubikstate.dat}%
+   \@printrubikstate% 
+   \@closestatefile% close data file
+   \typeout{---running Perl script}%
+   \immediate\write18{\rubikperlcmd}%
+   \typeout{---inputting NEW datafile (from Perl)}%
+   \input{rubikstateNEW.dat}%
+   \typeout{-----------------------------------------}%
+ }{\typeout{** ERROR: \rubikperlname\space does not exist}%
+}}
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+%
+% \subsection{SaveRubikState macro}
+%
+% \begin{macro}{\SaveRubikState} 
+% The command \cmd{\SaveRubikState}\marg{filename} saves the Rubik state
+% to a file.  Note that in order to actually write  a LaTeX
+% command to a file without a trailing space one must use the 
+%  \cmd{\string} command (see the book ``TeX by Topic'', p~238). 
+% Note that this macro uses the two internal commands \cmd{\Rubik@comment} 
+% and \cmd{\Rubik@print}.  \#1 is the output filename.
+% We use several \cmd{\typeout} commands to write to the log file.
+%    \begin{macrocode}
+\newcommand{\SaveRubikState}[1]{%
+\typeout{---NEW save command------------------}%
+\typeout{---command = SaveRubikState{#1}}%
+\typeout{---saving Rubik state data to file #1}%
+\immediate\openout\outfile=#1%
+\@print{\@comment filename: #1\@commentone}%
+\@print{\string\RubikFaceUp%
+   {\Ult}{\Umt}{\Urt}{\Ulm}{\Umm}{\Urm}{\Ulb}{\Umb}{\Urb}\@commentone}%
+\@print{\string\RubikFaceDown%
+   {\Dlt}{\Dmt}{\Drt}{\Dlm}{\Dmm}{\Drm}{\Dlb}{\Dmb}{\Drb}\@commentone}%
+\@print{\string\RubikFaceLeft%
+   {\Llt}{\Lmt}{\Lrt}{\Llm}{\Lmm}{\Lrm}{\Llb}{\Lmb}{\Lrb}\@commentone}%
+\@print{\string\RubikFaceRight%
+   {\Rlt}{\Rmt}{\Rrt}{\Rlm}{\Rmm}{\Rrm}{\Rlb}{\Rmb}{\Rrb}\@commentone}%
+\@print{\string\RubikFaceFront%
+   {\Flt}{\Fmt}{\Frt}{\Flm}{\Fmm}{\Frm}{\Flb}{\Fmb}{\Frb}\@commentone}%
+\@print{\string\RubikFaceBack%
+   {\Blt}{\Bmt}{\Brt}{\Blm}{\Bmm}{\Brm}{\Blb}{\Bmb}{\Brb}\@commentone}%
+\immediate\closeout\outfile%
+\typeout{-----------------------------------------}%
+}%
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+% --------------------------
+%    End of this package
+% --------------------------
+%    \begin{macrocode}
+%</rubikrotation>
+%    \end{macrocode}
+%
+%
+%
+%
+% \Finale
+%
+\endinput
+
+
+
+
+
diff --git a/Master/texmf-dist/source/latex/rubik/rubikrotation.ins b/Master/texmf-dist/source/latex/rubik/rubikrotation.ins
new file mode 100644
index 00000000000..3f1f2f1f354
--- /dev/null
+++ b/Master/texmf-dist/source/latex/rubik/rubikrotation.ins
@@ -0,0 +1,75 @@
+%% rubikrotation.ins 
+%% --- automatic overwriting of .sty is disabled-------
+%%  =========================================================
+%%  Authors: RWD Nickalls (dick@nickalls.org) 
+%%          and Apostolos Syropoulos (asyropoulos@yahoo.com)
+%%  Copyright January 20, 2014  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{rubikrotation.ins}
+\input docstrip.tex
+
+\preamble
+
+----------------------------------------------------------------- 
+  Authors: RWD Nickalls (dick@nickalls.org) 
+          and Apostolos Syropoulos (asyropoulos@yahoo.com)
+  Copyright January 2014  RWD Nickalls and 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 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{rubikrotation.sty}{\from{rubikrotation.dtx}{rubikrotation}}}
+
+%%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{*       rubikrotation.sty                             *}
+\Msg{*                                                     *}
+\Msg{* To produce the documentation run the file           *}
+\Msg{* rubikrotation.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---------------