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%%
%% example-cube.tex
%% package example using the rubikcube package
%% Requires the tikz package
%% January 20, 2014
%%--------NOTE-------------------------------------------
%% USAGE: (pdf)latex example-cube.tex
%%-------------------------------------------------------
\documentclass[a4paper]{article}
\usepackage{tikz} %% load tikz before rubikcube
\usepackage{rubikcube}
\usepackage{url}
\pagestyle{myheadings}
\markright{\textsc{rubikcube} package; \hspace{2cm}file = example-cube.tex}
%% increase textwidth to make room
\addtolength{\oddsidemargin}{-1.5cm}
\addtolength{\textwidth}{3cm}
%% brace and bracket
\newcommand{\Rubikbracket}[1]{$\left(\mbox{#1}\right)$}
\newcommand{\Rubikbrace}[1]{$\left\{\mbox{#1}\right\}$}
%%
\begin{document}
%%-------------------------
\subsection*{Example---the `superflip' configuration}
Once you have mastered Rubik's cube, then an interesting exercise is to generate
the so-called `superflip' configuration, in which all the corners are correctly
solved, while all the edges are flipped.
For the impatient, the superflip sequence of 24 quarter-turn rotations (listed on Randelshofer's website) is as follows. This converts the solved cube on the left into the configuration shown on the right.
\bigskip
\begin{center}
\RubikU\RubikR\RubikR\RubikFp\RubikR\RubikDp\RubikL\RubikBp\RubikR%
\RubikUp\RubikR\RubikUp\RubikD\RubikFp\RubikU\RubikFp\RubikUp\RubikDp%
\RubikB\RubikLp\RubikFp\RubikBp\RubikDp\RubikLp
\end{center}
\medskip
{\noindent}Surprisingly, this sequence is actually equivalent to
\Rubikbrace{\Rubikbracket{\RubikM\RubikUp}4, \Rubiky, \Rubikxp}3
\bigskip
\begin{figure}[hbt]
\centering
\RubikCubeSolved%
\begin{minipage}{2cm}
\begin{tikzpicture}[scale=0.5]
\DrawRubikCubeRU
\end{tikzpicture}
\end{minipage}
\hspace{5mm}$\Longrightarrow$\hspace{5mm}%
\RubikFaceUp {W}{R}{W} {B}{W}{G} {W}{O}{W}%
\RubikFaceDown {Y}{O}{Y} {B}{Y}{G} {Y}{R}{Y}%
\RubikFaceLeft {B}{W}{B} {R}{B}{O} {B}{Y}{B}%
\RubikFaceRight{G}{W}{G} {O}{G}{R} {G}{Y}{G}%
\RubikFaceFront{O}{W}{O} {B}{O}{G} {O}{Y}{O}%
\RubikFaceBack{R}{W}{R}
{G}{R}{B}
{R}{Y}{R}%
\begin{minipage}{2cm}
\begin{tikzpicture}[scale=0.5]
\DrawRubikCubeRU
\end{tikzpicture}
\end{minipage}
\hspace{1cm}%
\begin{minipage}{5cm}
\begin{tikzpicture}[scale=0.5]
\DrawRubikCubeFlat
\end{tikzpicture}
\end{minipage}
\caption{Two images of the superflip configuration.}
\end{figure}
The code for all this is given below---note that the facelet colours can be
written in various ways. Note also the trailing \% at the end of each line which is not inside a TikZ picture environment, and the value of placing each TikZ picture environment inside a minipage.
Since the default width of a Rubik cube is 4cm (see \S\,7 Fig~2 in \texttt{rubikcube.pdf}), then since the TikZ scale here is 0.5 then the required width of its minipage is equal to $0.5 \times 4\mbox{cm} = 2\mbox{cm}$.
%%----------
\begin{verbatim}
-------------------
\newcommand{\Rubikbracket}[1]{$\left(\mbox{#1}\right)$}
\newcommand{\Rubikbrace}[1]{$\left\{\mbox{#1}\right\}$}
\begin{center}
\RubikU\RubikR\RubikR\RubikFp\RubikR\RubikDp\RubikL\RubikBp\RubikR%
\RubikUp\RubikR\RubikUp\RubikD\RubikFp\RubikU\RubikFp\RubikUp\RubikDp%
\RubikB\RubikLp\RubikFp\RubikBp\RubikDp\RubikLp
\end{center}
\medskip
{\noindent}Surprisingly, this sequence is actually equivalent to
\Rubikbrace{\Rubikbracket{\RubikM\RubikUp}4, \Rubiky, \Rubikxp}3
\bigskip
\begin{figure}[hbt]
\centering
\RubikCubeSolved
\begin{minipage}{2cm}
\begin{tikzpicture}[scale=0.5]
\DrawRubikCubeRU
\end{tikzpicture}
\end{minipage}
\hspace{5mm}$\Longrightarrow$\hspace{5mm}%
\RubikFaceUp {Y}{B}{Y} {R}{Y}{O} {Y}{G}{Y}%
\RubikFaceDown {W}{G}{W} {R}{W}{O} {W}{B}{W}%
\RubikFaceLeft {R}{Y}{R} {B}{R}{G} {R}{W}{R}%
\RubikFaceRight{O}{Y}{O} {G}{O}{B} {O}{W}{O}%
\RubikFaceFront{G}{Y}{G} {R}{G}{O} {G}{W}{G}%
\RubikFaceBack {B}{Y}{B}%
{O}{B}{R}%
{B}{W}{B}%
\begin{minipage}{2cm}
\begin{tikzpicture}[scale=0.5]
\DrawRubikCubeRU
\end{tikzpicture}
\end{minipage}
\hspace{1cm}%
\begin{minipage}{5cm}
\begin{tikzpicture}[scale=0.5]
\DrawRubikCubeFlat
\end{tikzpicture}
\end{minipage}
\caption{Two images of the superflip configuration.}
\end{figure}
-------------------
\end{verbatim}
\subsection*{Using the rubikrotation package}
This is just a note to show that if this file were run in conjunction with the \texttt{rubikrotation} package, using the \LaTeX\ commandline switch \texttt{--shell-escape}, then the above figure could be generated more simply by replacing
\begin{verbatim}
\RubikFaceUp {Y}{B}{Y} {R}{Y}{O} {Y}{G}{Y}%
\RubikFaceDown {W}{G}{W} {R}{W}{O} {W}{B}{W}%
\RubikFaceLeft {R}{Y}{R} {B}{R}{G} {R}{W}{R}%
\RubikFaceRight{O}{Y}{O} {G}{O}{B} {O}{W}{O}%
\RubikFaceFront{G}{Y}{G} {R}{G}{O} {G}{W}{G}%
\RubikFaceBack {B}{Y}{B}%
{O}{B}{R}%
{B}{W}{B}%
\end{verbatim}
with the command
\begin{verbatim}
\RubikRotation{\superflip}%
\end{verbatim}
ie,~using instead the following code:
\begin{verbatim}
-----------------
\newcommand{\superflip}{U,R2,Fp,R,Dp,L,Bp,R,Up,R,Up,D,%
Fp,U,Fp,Up,Dp,B,Lp,Fp,Bp,Dp,Lp}
\begin{figure}[hbt]
\centering
\RubikCubeSolved%
\begin{minipage}{2cm}
\begin{tikzpicture}[scale=0.5]
\DrawRubikCubeRU
\end{tikzpicture}
\end{minipage}
\hspace{5mm}$\Longrightarrow$\hspace{5mm}%
\RubikRotation{\superflip}%
\begin{minipage}{2cm}
\begin{tikzpicture}[scale=0.5]
\DrawRubikCubeRU
\end{tikzpicture}
\end{minipage}
\hspace{1cm}%
\begin{minipage}{5cm}
\begin{tikzpicture}[scale=0.5]
\DrawRubikCubeFlat
\end{tikzpicture}
\end{minipage}
\caption{Two images of the superflip configuration.}
\end{figure}
-----------------
\end{verbatim}
\begin{center}
------ END ------
\end{center}
\end{document}
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