summaryrefslogtreecommitdiff
path: root/macros/latex/contrib/rubik/rubikpatterns.dtx
blob: 26995cce27e23c8514c8f934cbfbf3a62f6e4f46 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
% \iffalse meta-comment
%
% rubikpatterns.dtx
%
% version 5.0
%
% Authors: RWD Nickalls (dick@nickalls.org) 
%        and Apostolos Syropoulos (asyropoulos@yahoo.com)
%
% Copyright   25 February 2018  RWD Nickalls + A Syropoulos
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either
% version 1.3c of this license or (at your option) any
% later version. The latest version of this licence is in 
%
%       http://www.latex-project.org/lppl.txt
%
%<*readme>
%
% The rubikpatterns package provides a collection of LaTeX commands and macros 
% for the typesetting of Rubik cube configurations and rotation 
% sequences using the TikZ graphic language.
%
% Please report errors or suggestions for improvement to
%
%         Dick Nickalls or Apostolos Syropoulos
%
% This package requires the basic TikZ package to be loaded already
%</readme>
%
%<*driver>
\listfiles
\documentclass{ltxdoc}
\IfFileExists{rubikpatterns.sty}{\usepackage{rubikpatterns}}{%
    \GenericWarning{rubikpatterns.dtx}{Package file rubikpatterns.sty not found.
    Documentation will be messed up!^^J
    (Generate rubikpatterns.sty by (La)TeXing rubikpatterns.ins, and then^^J
    process rubikpatterns.dtx again)^^J}\stop
}%
\pagestyle{myheadings}
\markright{\texttt{rubikpatterns} \ \ (Rubik bundle v5.0, 2018) \ \ \texttt{www.ctan.org/pkg/rubik}}
\usepackage{ifpdf}
\usepackage{url,path}  %% for references and paths
\usepackage{graphicx}  %% for the two pdf figs
\usepackage{hypdoc}    %% for pdf bookmarks + hyperref documenting of packages
%%\OnlyDescription
\EnableCrossrefs
\PageIndex
\CodelineIndex
\CodelineNumbered
\RecordChanges
\setcounter{StandardModuleDepth}{1}
\begin{document}
  \DocInput{rubikpatterns.dtx}
  \PrintChanges
  \PrintIndex
\end{document}
%</driver>
% \fi
%
%
% 
%%% \CheckSum{187}
%
%%% \CharacterTable
%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%%   Digits        \0\1\2\3\4\5\6\7\8\9
%%   Exclamation   \!     Double quote  \"     Hash (number) \#
%%   Dollar        \$     Percent       \%     Ampersand     \&
%%   Acute accent  \'     Left paren    \(     Right paren   \)
%%   Asterisk      \*     Plus          \+     Comma         \,
%%   Minus         \-     Point         \.     Solidus       \/
%%   Colon         \:     Semicolon     \;     Less than     \<
%%   Equals        \=     Greater than  \>     Question mark \?
%%   Commercial at \@     Left bracket  \[     Backslash     \\
%%   Right bracket \]     Circumflex    \^     Underscore    \_
%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%%   Right brace   \}     Tilde         \~}
%
%
%
% \title{%
%       \ifpdf\pdfbookmark[1]{Title}{Title}\else\fi%
%       The \textsc{rubikpatterns} package}
%
% \author{
%      RWD Nickalls (dick@nickalls.org) \\
%     A Syropoulos (asyropoulos@yahoo.com)
%       }
%  \date{This file describes version \RPfileversion\ (\RPfiledate)\\
%  \texttt{www.ctan.org/pkg/rubik}}
%  \maketitle
%
%  \begin{abstract}
%  The \rubikpatterns\ package is a small data-base of well-known named 
%  Rubik patterns and associated rotation sequences, for use  in conjunction 
%  with the other Rubik `bundle' packages. 
%  \end{abstract}
%
%
%  \tableofcontents
%
% \pagebreak
%
% \section{Introduction}
%
%  The \textsc{rubikpatterns}  package is a small a data-base of well-known  Rubik 
%  rotation sequences  for use  in  conjunction with the Rubik bundle packages. 
%  These rotation sequences, which are well-known and  widely available, 
%  were  sourced from the Rubik-related
%  websites  of Reid M and Kociemba H (see References for URLs). 
%
%
%
%      \section{Requirements}
%
%  The \textsc{rubikpatterns} package requires (a)~the TikZ package, since it makes  
%  use  of the TikZ picture environment, (b)~the \textsc{rubikcube} package, and 
%  (c)~the \textsc{rubikrotation} package, since it uses
%  the Perl program \texttt{rubikrotation.pl}.
%  The \verb!TikZ! package must be loaded \textit{before} the \textsc{rubikcube}  package.
%  The \textsc{rubikrotation}  package  requires  Perl to be installed.
%
%
%
%   \section{Installation}
%
%
% The Rubik bundle consists of the four packages \textsc{rubikcube}, \textsc{rubikrotation},
% \textsc{rubikpatterns} and  \textsc{rubiktwocube}.
%
% Here we describe only the installation of the \textsc{rubikpatterns} package, 
% which  consists of the  following files:
%\begin{quote}
% \begin{verbatim}
% rubikpatterns.ins
% rubikpatterns.dtx
% rubikpatterns.pdf       --this document
% rubikpatternsLIST.tex
% rubikpatternsLIST.pdf   --a graphic list of all patterns in this package  
% rubikpatterns-doc-figA.pdf
%\end{verbatim}
%\end{quote}
% The package documentation is the file \texttt{rubikpatterns.pdf}.
%  The  style option \texttt{rubikpatterns.sty} is generated  by  running (pdf)\LaTeX\ on  
% the file \texttt{rubikpatterns.ins}  as follows:
%\begin{quote}
%\begin{verbatim}
%   pdflatex  rubikpatterns.ins 
%\end{verbatim}
%\end{quote}
% The documentation file (\texttt{rubikpatterns.pdf}) is then generated using the following 
% sequence of steps\,\footnote{Since the documentation includes a complicated indexing 
% system as well a \textsc{pdf} index and hyperef links (the package \texttt{hypdoc}
%  is used), then a lot of pdflatex runs are required. Prior to the first run it is
% a good idea to delete any relevant \texttt{.toc}, \texttt{.aux}, \texttt{.out} files.}:
%\begin{quote}
% \begin{verbatim}
%  pdflatex    rubikpatterns.dtx
%  pdflatex    rubikpatterns.dtx
%  makeindex -s gind.ist  rubikpatterns
%  makeindex -s gglo.ist -o rubikpatterns.gls  rubikpatterns.glo
%  pdflatex    rubikpatterns.dtx
%  pdflatex    rubikpatterns.dtx
%\end{verbatim}
%\end{quote}
%
%
% 
%  \subsection{Placing the files}
% \label{sec:placingfiles}
%
% Place the files either in a working directory, or where your system 
% will find them, e.g.,~in your \texttt{/texmf-local/} directory tree. 
% For example, on a Linux platform with a standard \TeX\ Directory Structure (TDS), then:
%
%\medskip
%{\noindent}*.sty  $\rightarrow$  \texttt{/usr/local/texlive/texmf-local/tex/latex/rubik/}
%{\newline}*.pdf  $\rightarrow$  \texttt{/usr/local/texlive/texmf-local/doc/rubik/}
%
%\medskip
%
%\medskip
%{\noindent}\textsc{file database}:\ \ Finally, (depending on your system) update the 
% \TeX\ file database. 
% For example, on a Linux platform  this is achieved using the \texttt{texhash} command.
%
% 
%  \subsection{The  rubikpatternsLIST file}
%

% Note that the package includes a  `rubikpatternsLIST' file (\texttt{rubikpatternsLIST.pdf}), 
% as well  as the source file  (\texttt{rubikpatternsLIST.tex}), and
%  associated  \texttt{.sh} (Linux) and \texttt{.bat} (Microsoft) batch 
% files, which can be used to facilitate processing the  source \texttt{.tex} file. 
% The file \texttt{rubikpatternsLIST.pdf} showcases the  Rubik cube 
% patterns made available in this package.
%
% Note that should you need to generate the file \texttt{rubikpatternsLIST.pdf} 
% from the  source file (\texttt{rubikpatternsLIST.tex}) you will require
% the \textsc{rubikcube} and  \textsc{rubikrotation} packages to be installed,
%  and will also need to use the \verb!--shell-escape! command-line 
% option  (see Section~\ref{sec:rubikrotation} for details). 
%
%
%
%
%
%       \subsection{Usage}
% \label{sec:usage}
% Load the  packages \textsc{rubikcube}, 
%  \textsc{rubikrotation} and \textsc{rubikpatterns} in the \TeX\ file preamble  \textit{after} loading 
% the TikZ package; for example, as follows: 
%\begin{quote}
% \begin{verbatim}
% \usepackage{tikz}
% \usepackage{rubikcube,rubikrotation,rubikpatterns}
%\end{verbatim}
%\end{quote}
% Since the sequence macros made available  by this package are accessed using commands 
% provided by the \textsc{rubikcube} and \textsc{rubikrotation} packages, please read the 
% documentation of these  packages.
%
%
% 
%   \section{Rubik patterns}
%
% A Rubik pattern  is the configuration generated by a sequence of rotations 
% (or `moves') from some initial starting configuration (typically a `solved' 
% configuration). For example, `sixspot' is a well known pattern  generated  
% from a solved Rubik cube by the  rotation sequence  
% \texttt{U,Dp,R,Lp,F,Bp,U,Dp}, as follows:
%
% \bigskip
%
% \noindent\begin{minipage}{\textwidth}
% \centering
% \ifpdf
%   \includegraphics[height=3cm]{rubikpatterns-doc-figA.pdf}
% \else
% \fi
% \end{minipage}
%
% \bigskip
%
% {\noindent}The code for the above image is as follows:
%
%\begin{verbatim}
% \noindent\hfil%
% \RubikCubeSolvedWB% 
% \ShowCube{2.4cm}{0.6}{\DrawRubikCubeRU}%
% \RubikRotation{\SixSpot}%
% \quad\SequenceBraceA{sixspot}{\ShowSequence{}{\Rubik}{\SequenceLong}}\quad%
% \ShowCube{2.4cm}{0.6}{\DrawRubikCubeRU}%
% \hfil%
%\end{verbatim}
%
% \bigskip
%
% Note that the  appearance of a pattern generated by  a given 
% rotation sequence is, of course, sensitive  to (a)~the particular colour 
% configuration of the solved cube used, and (b)~the initial  orientation of 
% the Rubik cube.
% 
% 
% Consequently the appearance generated  by a given sequence
% may appear  slightly different from 
% that on some websites, although the  colour configuration (pattern's \textit{geometry})   
% will, of course, be the same  (isomorphic). You may therefore need 
% to adjust the pre- (and possibly the post-)  x,y,z rotations in 
% order to obtain  a particular configuration as displayed elsewhere.
%
%
%  \subsection{Sequence macros}
%
% Each of the  rotation sequences of `patterns'  made available by the 
% \textsc{rubikpatterns} package is defined in  the file \texttt{rubikpatterns.sty}  
% in the following  compact macro form.
% For~example, the rotation sequence associated with the pattern known 
% as `SixSpot' (shown in the figure above) is defined as follows:
%\begin{verbatim}
%\newcommand{\SixSpot}{[SixSpot],U,Dp,R,Lp,F,Bp,U,Dp,<(8q*, 8f*)>}
%\newcommand{\sixspot}{\SixSpot}
%\end{verbatim}
% The macro name is \verb!\SixSpot! (the lower-case version \verb!\sixspot! can also be used). 
% Note that the second argument which 
% includes the  rotation sequence, also includes the pattern name in 
% square brackets \verb![SixSpot]!  as the first element in the sequence.
% Additional metadata (held by the macro \verb!\SequenceInfo!) is appended 
% in angle brackets (separated by a comma) as follows: \verb!<(8q*, 8f*)>!.
% For  details see  the \textsc{rubikrotation} package documentation.
%
%
%
%   \subsection{List of macros}
%
% The following is a list of the macro names of all the Rubik patterns supplied by
% the \textsc{rubikpatterns} package.  Note that for convenience each macro-name listed
% has an equivalent lower-case version. See the companion file \texttt{rubikpatternsLIST.pdf}
% for a detailed list  showing  each pattern  and its associated 
% sequence\,\footnote{We show all these images in a separate
% file (\texttt{rubikpatternsLIST.pdf}) purely because  generating them requires 
% using the \LaTeX\ command-line  option \texttt{--shell-escape} in conjunction 
% with the \textsc{rubikrotation} package.}. 
%
%  All the pattern names encoded here (as macros) are  well-known and widely available. 
% However, some pattern names have been slightly modified
% in order to avoid spaces and to keep them as similar to the original as possible.
% On finding different sequences which generate the same pattern, then the  
% shortest  sequence has been selected   (they can be readily distinguished by their metadata).
% 
% Finally, we note that there is a serious need for a standardised one-word nomenclature 
% in order to  avoid confusion, and to facilitate computerisation and an electronic database.
% Such a notation also needs to accommodate  those sequence variations which generate the same pattern.
% We welcome suggestions and/or help for improvement.

%
%\begin{verbatim}
%  \PonsAsinorum
%  \CheckerboardsThree
%  \CheckerboardsSix
%  \Stripes
%  \CubeInCube
%  \CubeInCubeInCube
%  \ChristmasCross
%  \PlummersCross
%  \Anaconda
%  \Python
%  \BlackMamba
%  \GreenMamba
%  \FemaleRattlesnake
%  \MaleRattlesnake
%  \FemaleBoa
%  \MaleBoa
%  \FourSpot
%  \SixSpot
%  \OrthogonalBars
%  \SixTs
%  \SixTwoOne
%  \ExchangedPeaks
%  \TwoTwistedPeaks
%  \FourTwistedPeaks
%  \ExchangedChickenFeet
%  \TwistedChickenFeet
%  \ExchangedRings
%  \TwistedRings
%  \EdgeHexagonTwo
%  \EdgeHexagonThree
%  \TomParksPattern
%  \RonsCubeInCube
%  \TwistedDuckFeet
%  \ExchangedDuckFeet
%  \Superflip
%\end{verbatim}
%
% Note that  the particular  superflip sequence made available by this package 
% (shown in \texttt{rubikpatternsLIST.pdf}) is due to  Reid (1995), and is detailed 
% on the Kociemba webpage  \texttt{http://www.kociemba.org/math/oh.htm}. Indeed, this was the 
% first sequence to define the `20-move' (HTM) upper boundary for solving a Rubik cube 
% (see  Rokicki \textit{et~al.}, 2013). 
%
% The superflip configuration is also significant  since it is its own inverse. 
% For example, the following two \verb!\RubikRotation! commands will generate the same 
% configuration (starting from a solved cube):
%\begin{verbatim}
% \RubikRotation{\superflip}
% \RubikRotation{\superflip,<inverse>}
%\end{verbatim}
% This property  is shown as  one of the examples in the Rubik bundle  file \texttt{rubikexamples.pdf}.
%
%
%
%     \section{Change history}
%
% \begin{itemize}
%
% \item Version 4.0 (March 2017)
%
% --- First release of this package.
%
% \end{itemize}
%
%
%
%   \section{References}
%     \label{sec:references}
%
%\begin{itemize}
%
% \item Fridrich website (Fridrich J). 
% See the `Pretty patterns'  webpage \url{http://www.ws.binghamton.edu/fridrich/ptrns.html}
%
% \item  Kociemba website (Kociemba H).  \url{http://www.kociemba.org/cube.htm}
% {\newline}---for superflip see: \url{http://www.kociemba.org/math/oh.htm}
%
% \item Randelshofer website (Randelshofer W).  Pretty patterns. 
% \url{http://www.randelshofer.ch/rubik/patterns/U080.01.html}
%
% \item Reid M. \  Patterns.  \url{http://www.cflmath.com/Rubik/patterns.html}
%
% \item Reid M. (1995). Superflip requires 20 face turns. (January 1995) 
%   \url{http://www.math.ucf.edu/~reid/Rubik/CubeLovers/} 
%  (see Section~\ref{sec:superflip})  
% {\newline}[cited from Rokicki \textit{et~al.}, 2013]. 
% {\newline}(Note: easier to use is the following html indexed version of the 
% archive of the Cube-Lovers usenet group (1982--1997)  
% \url{http://www.math.rwth-aachen.de/~Martin.Schoenert/Cube-Lovers/})
%
%  \item Rokicki T, Kociemba H, Davidson M and Dethridge J (2013). The diameter of the Rubik's 
%  cube is twenty.  \textit{SIAM.\ J.\ Discrete Math.}, \textbf{27}, 1082--1105. 
%   \url{http://tomas.rokicki.com/rubik20.pdf}
%
%\end{itemize}
% 
%
%
%
% ^^A ==================================================
% \StopEventually{\PrintIndex}
%
%
%
%        \section[The code]{The code (\texttt{rubikpatterns.sty})} 
%
% 
%   \subsection{Package heading}
%   \label{sec:CodePackageHeading}
%
%    \begin{macrocode}
%<*rubikpatterns>
\def\RPfileversion{5.0}%
\def\RPfiledate{2018/02/25}%  25 February 2018
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{rubikpatterns}[\RPfiledate\space (v\RPfileversion)]
%    \end{macrocode}
%
%
%    \begin{macro}{\rubikpatterns}
% First we create a suitable logo
%    \begin{macrocode}
\newcommand{\rubikpatterns}{\textsc{rubikpatterns}}
%    \end{macrocode}
%    \end{macro}
%
%   \subsection{Patterns}
%   \label{sec:patternscode}
%
%
%
%
%  \subsubsection{Superflip}
%   \label{sec:superflip}
%
% This particular superflip sequence is from the Kociemba website (his Oh webpage). 
% It is due to  Reid (1995).
%  \begin{macrocode}
\newcommand{\Superflip}{[Superflip],Dp,R2,Fp,D2,F2,U2,Lp,R,Dp,R2,B,F,Rp,%
U2,Lp,F2,Rp,U2,Rp,Up,<(20f*)>}%
\newcommand{\superflip}{\Superflip}
%    \end{macrocode}
%
%
%  \subsubsection{Reid data}
%
% These named sequences are derived from the Reid website. 
%  \begin{macrocode}
\newcommand{\PonsAsinorum}{[PonsAsinorum],F2,B2,R2,L2,U2,D2,%
   <(12q*, 6f*)>}%
\newcommand{\ponsasinorum}{\PonsAsinorum}%
\newcommand{\CheckerboardsThree}%
   {[CheckerboardsThree],F,B2,Rp,D2,B,R,U,Dp,R,Lp,Dp,Fp,R2,D,F2,Bp,%
   <(20q*, 16f*), order 3>}%  
\newcommand{\checkerboardsthree}{\CheckerboardsThree}%
\newcommand{\CheckerboardsSix}%
   {[CheckerboardsSix],R2,L2,U,B,L2,Dp,F,B2,R,Lp,Fp,B,R,D,F2,Lp,Up,%
   <(17f*, 22q), order 6>}%  
\newcommand{\checkerboardssix}{\CheckerboardsSix}%
\newcommand{\Stripes}{[Stripes],F,U,F,R,L2,B,Dp,R,D2,L,Dp,B,R2,L,F,U,F,%
   <(20q*, 17f*)>}%  
\newcommand{\stripes}{\Stripes}%
\newcommand{\CubeInCube}{[CubeInCube],F,L,F,Up,R,U,F2,L2,Up,Lp,B,Dp,Bp,L2,U,%
   <(18q*, 15f*)>}%  
\newcommand{\cubeincube}{\CubeInCube}%
\newcommand{\CubeInCubeInCube}%
   {[CubeInCubeInCube],Fp,U,Bp,Rp,U,F2,U2,Fp,Up,F,U2,D,Bp,Dp,R2,B2,Up,%
   <(17f*, 22q)>}%  
\newcommand{\cubeincubeincube}{\CubeInCubeInCube}%
\newcommand{\ChristmasCross}{[ChristmasCross],U,F,Bp,L2,U2,L2,Fp,B,U2,L2,U,%
   <(16q*, 11f*)>}%  
\newcommand{\christmascross}{\ChristmasCross}%
\newcommand{\PlummersCross}%
   {[PlummersCross],R2,Lp,D,F2,Rp,Dp,Rp,L,Up,D,R,D,B2,Rp,U,D2,%
   <(20q*, 16f*)>}%  
\newcommand{\plummerscross}{\PlummersCross}%
\newcommand{\Anaconda}{[Anaconda],L,U,Bp,Up,R,Lp,B,Rp,F,Bp,D,R,Dp,Fp,%
   <(14q*, 14f*)>}%  
\newcommand{\anaconda}{\Anaconda}%
\newcommand{\Python}{[Python],F2,Rp,Bp,U,Rp,L,Fp,L,Fp,B,Dp,R,B,L2,%
   <(16q*, 14f*)>}%  
\newcommand{\python}{\Python}%
\newcommand{\BlackMamba}{[BlackMamba],R,D,L,Fp,R,Lp,D,Rp,U,Dp,B,Up,Rp,Dp,%
   <(14q*, 14f*)>}%  
\newcommand{\blackmamba}{\BlackMamba}%
\newcommand{\GreenMamba}{[GreenMamba],R,D,R,F,Rp,Fp,B,D,Rp,Up,Bp,U,D2,%
   <(14q*, 13f*)>}%    
\newcommand{\greenmamba}{\GreenMamba}%
\newcommand{\FemaleRattlesnake}%
   {[FemaleRattlesnake],U2,Dp,L2,D,B,U,Bp,Rp,L2,U2,F,Up,F,R,%
   <(18q*, 14f*)>}%  
\newcommand{\femalerattlesnake}{\FemaleRattlesnake}%
\newcommand{\MaleRattlesnake}%
   {[MaleRattlesnake],Rp,Fp,U,Fp,U2,R,L2,B,Up,Bp,Dp,L2,U2,D,%
   <(18q*, 14f*)>}%  
\newcommand{\malerattlesnake}{\MaleRattlesnake}%
\newcommand{\FemaleBoa}{[FemaleBoa],R,Up,R2,U2,F,D2,R2,Up,Dp,R,Dp,Fp,%
   <(16q*, 12f*)>}%  
\newcommand{\femaleboa}{\FemaleBoa}%
\newcommand{\MaleBoa}{[MaleBoa],F,D,Rp,U,D,R2,D2,Fp,U2,R2,U,Rp,%
   <(16q*, 12f*)>}%  
\newcommand{\maleboa}{\MaleBoa}%
\newcommand{\FourSpot}{[FourSpot],F2,B2,U,Dp,R2,L2,U,Dp,%
   <(12q*, 8f*)>}%  
\newcommand{\fourspot}{\FourSpot}%
\newcommand{\SixSpot}{[SixSpot],U,Dp,R,Lp,F,Bp,U,Dp,%
   <(8q*, 8f*)>}%  
\newcommand{\sixspot}{\SixSpot}%
\newcommand{\OrthogonalBars}%
   {[OrthogonalBars],F,Rp,U,L,Fp,Lp,F,Up,R,U,Lp,Up,L,Fp,%
   <(14q*, 14f*)>}%  
\newcommand{\orthogonalbars}{\OrthogonalBars}%
\newcommand{\SixTs}{[SixTs],F2,R2,U2,Fp,B,D2,L2,F,B,%
   <(14q*, 9f*)>}% 
\newcommand{\sixts}{\SixTs}%
\newcommand{\SixTwoOne}{[SixTwoOne],U,B2,D2,L,Bp,Lp,Up,Lp,B,D2,B2,%
   <(15q*, 11f*)>}%  
\newcommand{\sixtwoone}{\SixTwoOne}%
\newcommand{\ExchangedPeaks}%
   {[ExchangedPeaks],F2,R2,D,R2,U,D,F2,Dp,Rp,Dp,F,L2,Fp,D,R,Up,%
   <(16f*, 21q)>}%  
\newcommand{\exchangedpeaks}{\ExchangedPeaks}%
\newcommand{\TwoTwistedPeaks}%
   {[TwoTwistedPeaks],F,D2,B,R,Bp,Lp,F,Dp,L2,F2,R,Fp,Rp,F2,Lp,Fp,%
   <(16f*, 20q)>}%
\newcommand{\twotwistedpeaks}{\TwoTwistedPeaks}%
\newcommand{\FourTwistedPeaks}%
   {[FourTwistedPeaks],Up,D,B,Rp,F,R,Bp,Lp,Fp,B,L,F,Rp,Bp,R,Fp,Up,D,%
   <(18q*, 18f*)>}%
\newcommand{\fourtwistedpeaks}{\FourTwistedPeaks}%
\newcommand{\ExchangedChickenFeet}%
   {[ExchangedChickenFeet],F,Lp,Dp,Bp,L,F,U,Fp,Dp,F,L2,Bp,Rp,U,L2,Dp,F,%
   <(19q*, 17f*)>}%
\newcommand{\exchangedchickenfeet}{\ExchangedChickenFeet}%
\newcommand{\TwistedChickenFeet}%
   {[TwistedChickenFeet],F,Lp,D,Fp,Up,B,U,F,Up,F,Rp,F2,L,Up,Rp,D2,%
   <(18q*, 16f*)>}%
\newcommand{\twistedchickenfeet}{\TwistedChickenFeet}%
\newcommand{\ExchangedRings}%
   {[ExchangedRings],F,U,Dp,Lp,B2,L,Up,D,F,U,R2,L2,Up,L2,F2,%
   <(15f*, 20q)>}%
\newcommand{\exchangedrings}{\ExchangedRings}%
\newcommand{\TwistedRings}%
   {[TwistedRings],F,D,Fp,D2,Lp,Bp,U,L,D,R,U,Lp,Fp,U,L,U2,%
   <(18q*, 16f*)>}%
\newcommand{\twistedrings}{\TwistedRings}%
\newcommand{\EdgeHexagonTwo}%
   {[EdgeHexagonTwo],U,B2,Up,Fp,Up,D,Lp,D2,L,U,Dp,F,Dp,L2,B2,Dp,%
   <(20q*, 16f*) order2>}% 
\newcommand{\edgehexagontwo}{\EdgeHexagonTwo}%
\newcommand{\EdgeHexagonThree}%
   {[EdgeHexagonThree],F,L,B,U,L,F2,B2,Rp,F2,B2,Up,Bp,Lp,Fp,%
   <(14f*, 18q) order 3>}%
\newcommand{\edgehexagonthree}{\EdgeHexagonThree}%
\newcommand{\TomParksPattern}%
   {[TomParksPattern],L,U,F2,R,Lp,U2,Bp,U,D,B2,L,F,Bp,Rp,L,Fp,R,%
   <(20q*, 17f*)>}%
\newcommand{\tomparkspattern}{\TomParksPattern}%
\newcommand{\RonsCubeInCube}%
   {[RonsCubeInCube],L2,D2,Lp,D2,B2,L2,B2,Lp,D2,L2,B2,Lp,B2,%
   <(13f*, 23q)>}%
\newcommand{\ronscubeincube}{\RonsCubeInCube}%
\newcommand{\TwistedDuckFeet}%
   {[TwistedDuckFeet],F,Rp,B,R,U,Fp,Lp,Fp,U2,Lp,Up,D2,B,Dp,F,Bp,U2,%
   <(20q*, 17f*)>}%
\newcommand{\twistedduckfeet}{\TwistedDuckFeet}%
\newcommand{\ExchangedDuckFeet}%
   {[ExchangedDuckFeet],U,F,R2,Fp,Dp,R,U,B2,U2,Fp,R2,F,D,B2,R,Bp,%
   <(21q*, 16f*)>}%
\newcommand{\exchangedduckfeet}{\ExchangedDuckFeet}%
%    \end{macrocode}
% --------------------------
%    End of this package
% --------------------------
%    \begin{macrocode}
%</rubikpatterns>
%    \end{macrocode}
%
%
%
%
% \Finale
%
\endinput