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-rw-r--r--Master/texmf-dist/tex/generic/pst-cox/pst-coxcoor.tex374
-rw-r--r--Master/texmf-dist/tex/generic/pst-cox/pst-coxeterp.tex986
2 files changed, 1360 insertions, 0 deletions
diff --git a/Master/texmf-dist/tex/generic/pst-cox/pst-coxcoor.tex b/Master/texmf-dist/tex/generic/pst-cox/pst-coxcoor.tex
new file mode 100644
index 00000000000..1cb59e7d978
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pst-cox/pst-coxcoor.tex
@@ -0,0 +1,374 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% polygonesCoordinate\pst-coxcoor.tex
+% Authors: J.-G. Luque and M. Luque
+% Purpose: Library pst-coxcoor.tex
+% Created: 02/02/2008
+% License: LGPL
+% Project: PST-Cox V1.00
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Copyright © 2008 Jean-Gabriel Luque, Manuel Luque.
+% This work may be distributed and/or modified under the condition of
+% the Lesser GPL.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% This file is part of PST-Cox V1.00.
+%
+% PST-Cox V1.00 is free software: you can redistribute it and/or modify
+% it under the terms of the Lesser GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+%
+% PST-Cox V1.00 is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% Lesser GNU General Public License for more details.
+%
+% You should have received a copy of the Lesser GNU General Public License
+% along with PST-Cox V1.00. If not, see <http://www.gnu.org/licenses/>.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\fileversion{0.98 Beta}
+\def\filedate{2008/14/01}
+
+\message{`Pst-Coxeter-Coordinates' v\fileversion, \filedate\space
+(Jean-Gabriel Luque and Manuel Luque)}
+
+\csname PstCoxeterCoordinatesLoaded\endcsname
+\let\PstCoxeterCoordinatesLoaded\endinput
+% Require PSTricks and pst-xkey
+\ifx\PSTnodeLoaded\endinput\else\input pstricks.tex\fi
+\ifx\PSTXKeyLoaded\endinput\else\input pst-xkey.tex\fi
+%
+% Catcodes changes.
+\edef\PstAtCode{\the\catcode`\@}
+\catcode`\@=11\relax
+
+\pst@addfams{pst-coxeter}
+ %%% Parameter choice. Allows to choice the polytope. To each integer
+ %%% 0<i<74 corresponds a polytope.
+\define@key[psset]{pst-coxeter}{choice}{%
+\pst@cntg=#1\relax \ifnum\pst@cntg>80 \typeout{choice < or = 80 and
+not `\the\pst@cntg'. Value 1 forced.} \pst@cntg=1
+ \fi
+\edef\psk@pstCoxeter@choice{#1}}
+\psset{choice=1}
+%
+%
+% Graphical parameters
+%
+% Colors
+% Color of Vertices
+% Example: \CoxeterCoordinates[colorVertices=blue,choice=5]
+\define@key[psset]{pst-coxeter}{colorVertices}{%
+\pst@getcolor{#1}\pscolorVertices}
+% by default the color of the vertices is green
+\psset{colorVertices=green}
+% Color of centers
+% Example: \CoxeterCoordinates[colorCenters=blue,choice=5]
+\define@key[psset]{pst-coxeter}{colorCenters}{%
+\pst@getcolor{#1}\pscolorCenters}
+ \psset{colorCenters=blue}
+% Color of centers of the faces
+% Example: \CoxeterCoordinates[colorCentersFaces=blue,choice=5]
+\define@key[psset]{pst-coxeter}{colorCentersFaces}{%
+\pst@getcolor{#1}\pscolorCentersFaces}
+ \psset{colorCentersFaces=red}
+%
+% Color of centers of the Cells
+% Example: \CoxeterCoordinates[colorCentersCells=blue,choice=5]
+\define@key[psset]{pst-coxeter}{colorCentersCells}{%
+\pst@getcolor{#1}\pscolorCentersCells}
+% by default the color of the centers is red.
+\psset{colorCentersCells=magenta}
+%
+%
+% Dot styles
+% style of Vertices
+% Example: \CoxeterCoordinates[styleVertices=*pentagon,P=5]
+\def\psset@styleVertices#1{%
+\@ifundefined{psds@#1}%
+{\@pstrickserr{styleVertices `#1' not defined}\@eha}%
+{\edef\psk@styleVertices{#1}}}
+% by default the vertices are represented by a (empty) circle (styleVertices=o)
+ \psset@styleVertices{o}
+% style of Centers
+% Example: \CoxeterCoordinates[styleCenters=*pentagon,choice=5]
+\def\psset@styleCenters#1{%
+\@ifundefined{psds@#1}%
+{\@pstrickserr{styleCenters `#1' not defined}\@eha}%
+{\edef\psk@styleCenters{#1}}}
+% by default the vertices are represented by a disk (styleVertices=*)
+ \psset@styleCenters{*}
+%
+% style of Centers of the faces
+% Example: \CoxeterCoordinates[styleCentersFaces=*pentagon,choice=5]
+%
+\def\psset@styleCentersFaces#1{%
+\@ifundefined{psds@#1}%
+{\@pstrickserr{styleCentersFaces `#1' not defined}\@eha}%
+{\edef\psk@styleCentersFaces{#1}}}
+%
+% by default the centers of the faces are represented by a disk (styleCentersFaces=*)
+%
+ \psset@styleCentersFaces{*}
+ % style of Centers of the Cells
+% Example: \CoxeterCoordinates[styleCentersCells=*pentagon,choice=5]
+\def\psset@styleCentersCells#1{%
+\@ifundefined{psds@#1}%
+{\@pstrickserr{styleCentersCells `#1' not defined}\@eha}%
+{\edef\psk@styleCentersCells{#1}}}
+% by default the centers of the cells are represented by a disk (stylesCentersCells=*)
+ \psset@styleCentersCells{*}
+%
+%
+% Dot sizes
+% Size of vertices
+% Example: \CoxeterCoordinates[sizeVertices=0.1,choice=5]
+\newdimen\pssizeVertices
+\def\psset@sizeVertices#1{\pssetlength\pssizeVertices{#1}}
+\psset@sizeVertices{0.05}
+% Sizes of centers
+% Example: \CoxeterCoordinates[sizeCenters=0.1,choice=5]
+\newdimen\pssizeCenters
+\def\psset@sizeCenters#1{\pssetlength\pssizeCenters{#1}}
+\psset@sizeCenters{0.05}
+%
+% Sizes of centers of the faces
+% Example: \CoxeterCoordinates[sizeCentersFaces=0.1,choice=5]
+%
+\newdimen\pssizeCentersFaces
+\def\psset@sizeCentersFaces#1{\pssetlength\pssizeCentersFaces{#1}}
+\psset@sizeCentersFaces{0.05}
+%
+% Sizes of centers of the cells
+% Example: \CoxeterCoordinates[sizeCentersCells=0.1,choice=5]
+%
+\newdimen\pssizeCentersCells
+\def\psset@sizeCentersCells#1{\pssetlength\pssizeCentersCells{#1}}
+\psset@sizeCentersCells{0.05}%
+%
+\newif\ifPst@drawvertices
+\define@key[psset]{pst-coxeter}{drawvertices}[true]{%
+\@nameuse{Pst@drawvertices#1}}
+%
+\newif\ifPst@drawedges
+\define@key[psset]{pst-coxeter}{drawedges}[true]{%
+\@nameuse{Pst@drawedges#1}}
+%
+\newif\ifPst@drawcenters
+\define@key[psset]{pst-coxeter}{drawcenters}[true]{%
+\@nameuse{Pst@drawcenters#1}}
+%
+%
+\newif\ifPst@drawcentersfaces
+\define@key[psset]{pst-coxeter}{drawcentersfaces}[false]{%
+\@nameuse{Pst@drawcentersfaces#1}}
+%
+%
+\newif\ifPst@drawcenterscells
+\define@key[psset]{pst-coxeter}{drawcenterscells}[false]{%
+\@nameuse{Pst@drawcenterscells#1}}
+%
+\psset{drawvertices=true,drawedges=true,drawcenters=true}
+%
+%% Prologue for postscript
+\pstheader{pst-coxeter.pro}
+%
+% definition if the macro \CoxeterCoordinates
+%
+\def\CoxeterCoordinates{\pst@object{CoxeterCoordinates}}
+\def\CoxeterCoordinates@i{\@ifnextchar[{\CoxeterCoordinates@do}{\CoxeterCoordinates@do[]}}
+\def\CoxeterCoordinates@do[#1]{{%
+\psset{#1}%
+\begin@ClosedObj
+\addto@pscode{%
+%
+% List of the polytopes
+% The option choice allows to choice the polytope
+% Each values of choice corresponds to a variable cox***datas
+% The variables cox***datas are defined in the file pst-coxcoor.pro
+%
+/choice \the\pst@cntg\space def
+ choice 1 eq {cox233datas} if
+ choice 2 eq {cox332datas} if
+ choice 3 eq {cox333datas} if
+ choice 4 eq {cox342datas} if
+ choice 5 eq {cox344datas} if
+ choice 6 eq {cox343datas} if
+ choice 7 eq {cox434datas} if
+ choice 8 eq {cox24333datas} if
+ choice 9 eq {cox33333datas} if
+ choice 10 eq {cox33342datas} if
+ choice 11 eq {cox3333333datas} if
+ choice 12 eq {cox382datas} if
+ choice 13 eq {cox283datas} if
+ choice 14 eq {cox353datas} if
+ choice 15 eq {cox443datas} if
+ choice 16 eq {cox432datas} if
+ choice 17 eq {cox234datas} if
+ choice 18 eq {cox264datas} if
+ choice 19 eq {cox462datas} if
+ choice 20 eq {cox535datas} if
+ choice 21 eq {cox2103datas} if
+ choice 22 eq {cox3102datas} if
+ choice 23 eq {cox253datas} if
+ choice 24 eq {cox352datas} if
+ choice 25 eq {cox243datas} if
+ choice 26 eq {cox23243datas} if
+ choice 27 eq {cox34232datas} if
+ choice 28 eq {cox3423232datas} if
+ choice 29 eq {cox2323243datas} if
+ choice 30 eq {cox23252datas} if
+ choice 31 eq {cox25232datas} if
+ choice 32 eq {cox2323242datas} if
+ choice 33 eq {cox2423232datas} if
+ choice 34 eq {cox2324232datas} if
+ choice 35 eq {cox2323252datas} if
+ choice 36 eq {cox2523232datas} if
+ choice 37 eq {cox3523datas} if %
+ choice 38 eq {cox5525datas} if
+ choice 39 eq {cox2523datas} if
+ choice 40 eq {cox3522datas} if
+ choice 41 eq {cox31032datas} if
+ choice 42 eq {cox21033datas} if
+ choice 43 eq {cox3832datas} if
+ choice 44 eq {cox2833datas} if
+ choice 45 eq {cox562datas} if
+ choice 46 eq {cox265datas} if
+ choice 47 eq {cox4833datas} if
+ choice 48 eq {cox3834datas} if
+ choice 49 eq {cox552datas} if
+ choice 50 eq {cox255datas} if
+ choice 51 eq {cox51032datas} if
+ choice 52 eq {cox21035datas} if
+ choice 53 eq {cox532datas} if
+ choice 54 eq {cox235datas} if
+ choice 55 eq {cox542datas} if
+ choice 56 eq {cox245datas} if
+choice 57 eq {cox51033datas} if
+ choice 58 eq {cox31035datas} if
+ choice 59 eq {cox543datas} if
+ choice 60 eq {cox345datas} if
+choice 61 eq {cox533datas} if
+ choice 62 eq {cox335datas} if
+ choice 63 eq {cox5523datas} if
+ choice 64 eq {cox3525datas} if
+ choice 65 eq {cox252232datas} if
+ choice 66 eq {cox232522datas} if
+ choice 67 eq {cox252252datas} if
+ choice 68 eq {cox252522datas} if
+ choice 69 eq {cox263datas} if
+ choice 70 eq {cox362datas} if
+ choice 71 eq {cox25223232datas} if
+ choice 72 eq {cox23232522datas} if
+ choice 73 eq {cox23252252datas} if
+ choice 74 eq {cox23252522datas} if
+ choice 75 eq {cox25223252datas} if
+ choice 76 eq {cox25225232datas} if
+ choice 77 eq {cox25232522datas} if
+ choice 78 eq {cox25252232datas} if
+ choice 79 eq {cox25252252datas} if
+ choice 80 eq {cox252252522datas} if
+ %%% <-- add new polytope here
+ 0 0 translate
+ %%% Usefull definitions
+/pscolorVertices {\pst@usecolor\pscolorVertices currentrgbcolor} def
+/pscolorCenters {\pst@usecolor\pscolorCenters currentrgbcolor} def
+ /pscolorCentersFaces {\pst@usecolor\pscolorCentersFaces currentrgbcolor} def
+ /pscolorCentersCells {\pst@usecolor\pscolorCentersCells currentrgbcolor} def
+/unit \pst@number\psunit\space def % pts -> cm
+/unit \pst@number\psunit\space def % pts -> cm
+1 setlinejoin
+ %%%% Drawing the edges
+\ifPst@drawedges
+ 0 1 NbrEdges 1 sub { % from 0 to nbedges-1 (draw all the edges)
+ /CompteurVertices ED
+ /CompteurIntermediaireSommets CompteurVertices NbrVerticesInAnEdge mul
+ def
+newpath ListePoints CompteurIntermediaireSommets get aload pop
+ /Y exch def /X exch def
+ X unit mul Y unit mul moveto
+1 1 NbrVerticesInAnEdge 1 sub { % from 1 to nbvertices in an edge -1
+ /CompteurEdges ED
+ListePoints CompteurIntermediaireSommets CompteurEdges add get aload
+pop
+ /Y exch def /X exch def
+ X unit mul Y unit mul lineto
+ }
+ for
+closepath stroke } for \fi %
+ %%%% Drawing of the Vertices
+/DS \pst@number\pssizeVertices\space def
+\@nameuse{psds@\psk@styleVertices}%
+\ifPst@drawvertices
+% We draw all the vertices of all edges
+0 1 NbrEdges NbrVerticesInAnEdge mul 1 sub { % From 0 to nbEdges*NbVerticesInEdges-1
+/CompteurEdges ED
+ ListePoints CompteurEdges get aload pop
+ /Y exch def /X exch def
+ pscolorVertices
+ X unit mul Y unit mul
+ Dot
+ stroke
+} for
+ \fi
+%
+% Drawing of the Centers of the Faces
+%
+/DS \pst@number\pssizeCentersFaces\space def
+\@nameuse{psds@\psk@styleCentersFaces}%
+\ifPst@drawcentersfaces
+0 1 NbrFaces 1 sub{ % from 0 to NbrFaces-1
+/CompteurFaces ED
+ ListeFaces CompteurFaces get aload pop
+ /Y exch def /X exch def
+ pscolorCentersFaces
+ X unit mul Y unit mul
+ Dot
+ stroke
+} for
+ \fi
+%
+% Drawing the centers of the Cells
+%
+/DS \pst@number\pssizeCentersCells\space def
+\@nameuse{psds@\psk@styleCentersCells}%
+\ifPst@drawcenterscells
+0 1 NbrCells 1 sub{ % from 0 to nbCells-1
+/CompteurCells ED
+ ListeCells CompteurCells get aload pop
+ /Y exch def /X exch def
+ pscolorCentersCells
+ X unit mul Y unit mul
+ Dot
+ stroke
+} for \fi
+%
+% Drawing the centers of the Edges
+%
+ /DS \pst@number\pssizeCenters\space def
+\@nameuse{psds@\psk@styleCenters}%
+\ifPst@drawcenters
+0 1 NbrEdges 1 sub { % from 0 to NbrEdges -1
+ /CompteurVertices ED
+ /CompteurIntermediaireSommets CompteurVertices NbrVerticesInAnEdge mul
+ def
+ /XM 0 def /YM 0 def
+0 1 NbrVerticesInAnEdge 1 sub { %
+ /CompteurEdges ED
+ ListePoints CompteurEdges CompteurIntermediaireSommets add get aload pop
+ /Y ED /X ED
+ /XM XM X add def
+ /YM YM Y add def
+ }
+ for
+ pscolorCenters
+ XM NbrVerticesInAnEdge div unit mul YM NbrVerticesInAnEdge div unit mul %1.5 0 360 arc
+ Dot
+ stroke
+} for \fi
+}%
+\end@ClosedObj
+}}
+\catcode`\@=\PstAtCode\relax
+\endinput
+%%
+%% END: pst-coxeter3.tex
diff --git a/Master/texmf-dist/tex/generic/pst-cox/pst-coxeterp.tex b/Master/texmf-dist/tex/generic/pst-cox/pst-coxeterp.tex
new file mode 100644
index 00000000000..32cccc28889
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pst-cox/pst-coxeterp.tex
@@ -0,0 +1,986 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% pst-coxeter_parameter\pst-coxeterp.tex
+% Authors: J.-G. Luque and M. Luque
+% Purpose: Listing of the macros of pst-coxeterp
+% Created: 02/02/2008
+% License: LGPL
+% Project: PST-Cox V1.00
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Copyright © 2008 Jean-Gabriel Luque, Manuel Luque.
+% This work may be distributed and/or modified under the condition of
+% the Lesser GPL.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% This file is part of PST-Cox V1.00.
+%
+% PST-Cox V1.00 is free software: you can redistribute it and/or modify
+% it under the terms of the Lesser GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+%
+% PST-Cox V1.00 is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% Lesser GNU General Public License for more details.
+%
+% You should have received a copy of the Lesser GNU General Public License
+% along with PST-Cox V1.00. If not, see <http://www.gnu.org/licenses/>.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\fileversion{0.98 Beta}
+\def\filedate{2008/21/01}
+
+\message{`pst-Coxeter-parameter' v\fileversion, \filedate\space
+(Jean-Gabriel Luque and Manuel Luque)}
+
+\csname PstCoxeterLoaded\endcsname
+\let\PstCoxeter\endinput
+% Require PSTricks and pst-xkey
+\ifx\PSTnodeLoaded\endinput\else\input pstricks.tex\fi
+\ifx\PSTXKeyLoaded\endinput\else\input pst-xkey.tex\fi
+%
+% Catcodes changes.
+\edef\PstAtCode{\the\catcode`\@}
+\catcode`\@=11\relax
+%
+%define the family of parameters pst-coxeter-parameter
+%
+\pst@addfams{pst-coxeter-parameter}
+%
+% There is two parameters P and Q which encodes the angle
+% between the mirrors. The parameter P is used for the regular polygons
+% the polytopes gamma^p_n, beta^p_n, gamma^p_2 and beta^p_2
+% Example: \Polygon[P=5]
+%
+\define@key[psset]{pst-coxeter-parameter}{P}{%
+\edef\psk@pstCoxeter@P{#1}}
+%
+\psset{P=6}
+%
+% The parameter Q is used for starry regular polygon.
+% Example: \Polygon[P=5,Q=2]
+%
+\define@key[psset]{pst-coxeter-parameter}{Q}{%
+\edef\psk@pstCoxeter@Q{#1}}
+%
+%
+\psset{Q=1}
+%
+% The dimension is used for simplices, polytopes gamma^p_n and beta^p_n
+% Example: \Simplex[dimension=4]
+%
+\define@key[psset]{pst-coxeter-parameter}{dimension}{%
+\edef\psk@pstCoxeter@dimension{#1}}
+\psset{dimension=3}
+%
+% Graphical parameters
+%
+% Colors
+% Color of Vertices
+% Example: \Polygon[colorVertices=blue,P=5]
+\define@key[psset]{pst-coxeter-parameter}{colorVertices}{%
+\pst@getcolor{#1}\pscolorVertices}
+% by default the color of the vertices is green
+\psset{colorVertices=green}
+% Color of centers
+% Example: \Polygon[colorCenters=blue,P=5]
+\define@key[psset]{pst-coxeter-parameter}{colorCenters}{%
+\pst@getcolor{#1}\pscolorCenters}
+%
+% by default the color of the centers is red.
+\psset{colorCenters=red}
+%
+%
+% Dot styles
+% style of Vertices
+% Example: \Polygon[styleVertices=*pentagon,P=5]
+\def\psset@styleVertices#1{%
+\@ifundefined{psds@#1}%
+{\@pstrickserr{styleVertices `#1' not defined}\@eha}%
+{\edef\psk@styleVertices{#1}}}
+% by default the vertices are represented by a (empty) circle (styleVertices=o)
+ \psset@styleVertices{o}
+% style of Centers
+% Example: \Polygon[styleCenters=*pentagon,P=5]
+\def\psset@styleCenters#1{%
+\@ifundefined{psds@#1}%
+{\@pstrickserr{styleCenters `#1' not defined}\@eha}%
+{\edef\psk@styleCenters{#1}}}
+% by default the vertices are represented by a disk (styleVertices=*)
+ \psset@styleCenters{*}
+%
+% Dot sizes
+% Size of vertices
+% Example: \Polygon[sizeVertices=0.1,P=5]
+\newdimen\pssizeVertices
+\def\psset@sizeVertices#1{\pssetlength\pssizeVertices{#1}}
+\psset@sizeVertices{0.05}
+% Sizes of centers
+% Example: \Polygon[sizeCenters=0.1,P=5]
+\newdimen\pssizeCenters
+\def\psset@sizeCenters#1{\pssetlength\pssizeCenters{#1}}
+\psset@sizeCenters{0.05}
+%
+% Boolean parameters
+%
+% The vertices are drawn only if the value of drawvertices is true
+% Examples: \Polygon[drawvertices=false,P=5]
+
+\newif\ifPst@drawvertices
+\define@key[psset]{pst-coxeter-parameter}{drawvertices}[true]{%
+\@nameuse{Pst@drawvertices#1}}
+%
+% The edges are drawn only if the value of drawedges is true
+% Examples: \Polygon[drawedges=false,P=5]
+%
+\newif\ifPst@drawedges
+\define@key[psset]{pst-coxeter-parameter}{drawedges}[true]{%
+\@nameuse{Pst@drawedges#1}}
+%
+%%
+% The centers are drawn only if the value of drawcenters is true
+%% Examples: \Polygon[drawcenters=false,P=5]
+%
+\newif\ifPst@drawcenters
+\define@key[psset]{pst-coxeter-parameter}{drawcenters}[true]{%
+\@nameuse{Pst@drawcenters#1}}
+%
+% By default the vertices, edges and centers are drawn.
+%
+%\setkeys{psset}{drawvertices=true,drawedges=true,drawcenters=true}
+\psset{drawvertices=true,drawedges=true,drawcenters=true}
+%
+% All the polytopes are encoded with the same way.
+% For each kind of polytope, we have wrote three procedures:
+% /drawVertices which allows to draw the vertices of the polytope
+% /drawEdges which allows to draw the edges of the polytope
+% /drawCenter which allows to draw the centers of the edges of the polytope
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%% LIST OF THE POLYTOPES
+%%
+% Regular real polygons
+%
+%
+% It is a well known family of polytope with two parameters P and Q.
+% This is the set of the classical polygons whose symmetric groups are dihedral 2[p]2.
+% Use the macro \Polygon[P=p,Q=q] draw the polygon 2{p/q}2 in the notation of Coxeter.
+% The non starry real polygons are obtained when Q=1
+% The starry polygon are obtained when Q do not divided P
+%
+% Example:
+% \Polygon[P=5] draw a pentagone
+% \Polygon[P=5,Q=2] draw a regular star with five vertices.
+\def\Polygon{\pst@object{Polygon}}
+\def\Polygon@i{\@ifnextchar[{\Polygon@do}{\Polygon@do[]}}
+\def\Polygon@do[#1]{{%
+\pst@killglue
+\setkeys{psset}{#1}%
+\begin@ClosedObj
+\addto@pscode{%
+%%%% macro for the colors of the vertices and the centers
+/pscolorVertices {\pst@usecolor\pscolorVertices currentrgbcolor} def
+/pscolorCenters {\pst@usecolor\pscolorCenters currentrgbcolor} def
+ 0 0 translate
+%%% some usefull definition
+/unit \pst@number\psunit\space def % pts -> cm
+/Pi 180 def %%% use Pi instead of 180°
+/p \psk@pstCoxeter@P\space def % parameter P
+/q \psk@pstCoxeter@Q\space def % parameter Q
+/p_1 p 1 sub def % p-1
+1 setlinejoin CLW setlinewidth%
+%%%%% List of the vertices
+%%%%%
+ /TableauxPoints [
+0 1 p 1 add {%
+ /n exch def
+ [
+ 2 n Pi q mul mul mul p div cos % cos(2nqPi/p)
+ unit mul % pts to cm
+ 2 n Pi q mul mul mul p div sin % sin(2nPi/p)
+ unit mul % pts to cm
+ ]
+ } for
+] def
+%
+%
+%%%% Procedures
+%
+% /drawEdges: this procedure draws the edges
+%
+/drawEdges { 0 1 p {
+ /n exch def
+ TableauxPoints n get aload pop
+ /YL ED /XL ED
+ XL YL moveto % move to the point n of the array
+ TableauxPoints n 1 add get aload pop
+ lineto % draw a line from the point n to the point n+1
+ stroke
+ } for
+} def \ifPst@drawedges
+ drawEdges
+ stroke
+\fi
+ %%%%%%%%%%%%%%%%%%
+ % /drawVertices:this procedure draw the vertices
+ %
+ %
+/DS \pst@number\pssizeVertices\space def
+\@nameuse{psds@\psk@styleVertices}%
+/drawVertices {%
+ /Liste exch def
+ 0 1 p {
+ /compteur exch def
+ pscolorVertices
+ Liste compteur get aload pop
+ Dot
+ } for
+} def \ifPst@drawvertices
+ TableauxPoints drawVertices
+\fi
+ %%%%%%%%%%%%%%
+% /drawCenters : draw the centers of the edges
+%
+/DS \pst@number\pssizeCenters\space def
+\@nameuse{psds@\psk@styleCenters}%
+/drawCenters {
+ 0 1 p {
+ /n exch def
+ TableauxPoints n get aload pop
+ /YL ED /XL ED
+ TableauxPoints n 1 add get aload pop
+ /YR ED /XR ED
+ /YM YL YR add 2 div def % YM = (YL+YR)/2
+ /XM XL XR add 2 div def % XM = (XL+XR)/2
+ pscolorCenters
+ XM YM
+ Dot
+ stroke
+}for
+ } def
+\ifPst@drawcenters
+ drawCenters
+\fi
+}%
+\end@ClosedObj
+}}
+%
+%%%%%%%%%%%%%%%%%%% The simplices
+% Simplices are the real regular polytopes whose
+% roots system is A_{n+1}. The reflection groups which generates
+% it is the symmetric group (order (n+1)!).
+% Simplices are auto-reciprocal polytopes. The first examples are the tetrahedral (for dimension 2),
+% the pentatope (in dimension 4), the sextatope in dimension 5 etc.
+% In general the number of cells of dimension m ($m<n$) is equal to the binomial $\left(n+1\atop m+1\right)$.
+% Each cell is a simplex of dimension $m$.
+% For example, the tetrahedral has $4$ vertices, $6$ edges and $4$ faces; the pentatope has $5$ vertices, $10$ edges,
+% $10$ faces and $5$ cells of dimension $3$.
+%
+% Use the macro \Simplex to draw the projection of a simplex.
+% Use the parameter dimension to choose the dimension of the simplex.
+%
+% Example: \Simplex[dimension=5]
+%
+\def\Simplex{\pst@object{Simplex}}
+\def\Simplex@i{\@ifnextchar[{\Simplex@do}{\Simplex@do[]}}
+\def\Simplex@do[#1]{{%
+\pst@killglue
+\setkeys{psset}{#1}%
+\begin@ClosedObj
+\addto@pscode{%
+% Some usefull definitions
+/pscolorVertices {\pst@usecolor\pscolorVertices currentrgbcolor} def
+/pscolorCenters {\pst@usecolor\pscolorCenters currentrgbcolor} def 0
+0 translate
+/unit \pst@number\psunit\space def % pts -> cm
+/Pi 180 def
+/p \psk@pstCoxeter@dimension\space 1 add def % dimension of the space plus 1
+/p_1 p 1 sub def % dimension of the space
+1 setlinejoin CLW setlinewidth%
+%%%% Computation if the array of the Vertices
+ /TableauxPoints [
+0 1 p 1 add {% for n from 0 to p+1
+ /n exch def
+ 1 1 p 1 sub{ % for m from 1 to p+1
+ /m exch def
+ [
+ 2 n Pi mul mul p div cos % cos(2nPi/p)
+ unit mul % pts to cm
+ 2 n Pi mul mul p div sin % sin(2nPi/p)
+ unit mul % pts to cm
+ ]
+ [
+ 2 n m add Pi mul mul p div cos % cos(2nPi/p)
+ unit mul % pts to cm
+ 2 n m add Pi mul mul p div sin % sin(2nPi/p)
+ unit mul % pts to cm
+ ]
+ }for
+ } for
+] def
+%
+%%%%%% Procedure
+% /drawEdges : draw the edges of the simplex
+% One use the array TableauxPoints
+/drawEdges { 0 1 p p mul { % for n from 0 to p^2
+ /n exch def
+ TableauxPoints n 2 mul get aload pop % the point 2n of the array
+ /YL ED /XL ED
+ XL YL moveto
+ TableauxPoints n 2 mul 1 add get aload pop % the point 2n+1 of the array
+ lineto
+ stroke
+ } for
+} def \ifPst@drawedges
+ drawEdges
+ stroke
+\fi
+%
+% /drawVertices : draw the vertices of the simplex
+%
+/DS \pst@number\pssizeVertices\space def% define the size of the dots
+\@nameuse{psds@\psk@styleVertices}% style of the dots
+/drawVertices {%
+ /Liste exch def
+ 0 1 p p mul { % for compteur from 0 to p^2
+ /compteur exch def
+ pscolorVertices % color of the parameters colorVertices
+ Liste compteur get aload pop
+ Dot % draw a dot
+ } for
+} def \ifPst@drawvertices
+ TableauxPoints drawVertices % apply drawVertices to TableauxPoints
+\fi
+%
+% /drawCenters : draw the centers of the simplex
+%
+/DS \pst@number\pssizeCenters\space def % define the size of the dots
+\@nameuse{psds@\psk@styleCenters}% style of the dots
+/drawCenters {
+ 0 1 p p mul { % from n from 0 to p^2
+ /n exch def
+ TableauxPoints n 2 mul get aload pop % point $2n$ of TableauxPoints
+ /YL ED /XL ED
+ TableauxPoints n 2 mul 1 add get aload pop % point $2n+1$ of TableauxPoints
+ /YR ED /XR ED
+ /YM YL YR add 2 div def % YM:=(YL+YZ)/2
+ /XM XL XR add 2 div def % XM:=(XY+XZ)/2
+ pscolorCenters
+ XM YM
+ Dot
+ stroke
+}for
+ } def
+\ifPst@drawcenters
+ drawCenters
+\fi
+}
+\end@ClosedObj
+}}
+%
+%%%%%%%%%%%%%%%%%% The polytopes $\gamma^p_n$
+% These polytopes are complex polytopes $p\{4\}2\{3\}2\dots 2\{3\}2$ in the notation of Coxeter.
+% This means that their symmetric group is a $n!p$ order group generated by $n$ reflections
+% with relations $R_1^p=R_2^2=\dots R_n^2=Id$
+% $R_1R_2R_1R_2=R_2R_1R_2R_1$, $R_iR_{i+1}R_i=R_{i+1}R_i$ if i>1, $R_iR_j=R_jR_i$ if $|i-j|>1$.
+% Such a complex polytope has $\left(n\atop m\right)p^n$ cells of dimension $m$ ($m<n$) which are
+% complex polytopes $\gamma^p_m$.
+% When $p=2$, the polytope $\gamma^2_n$ is an hypercube.
+% When $p>2$, the polytope is not a real polytope since $R_1^2\neq Id$.
+% In this case, the edges are regular polygons with $p$ vertices.
+% When $n=2$, the projection is not convenient since the projection of some vertices are the same.
+% For an other projection, use the macro \gammaptwo described below.
+%
+% The two parameters are the dimension and $p$.
+%
+% Use the macro \gammapn[dimension=...,P=...] to draw the projection of a polytope $\gamma^p_n$.
+%
+% Example : \gammapn[dimension=5,P=4]
+%
+\def\gammapn{\pst@object{gammapn}}
+\def\gammapn@i{\@ifnextchar[{\gammapn@do}{\gammapn@do[]}}
+\def\gammapn@do[#1]{{%
+\pst@killglue
+\setkeys{psset}{#1}%
+\begin@ClosedObj
+\addto@pscode{%
+%%% Some usefull definitions
+/pscolorVertices {\pst@usecolor\pscolorVertices currentrgbcolor} def
+ /pscolorCenters {\pst@usecolor\pscolorCenters currentrgbcolor} def
+0 0 translate
+/unit \pst@number\psunit\space def % pts -> cm
+/Pi 180 def
+/p \psk@pstCoxeter@P\space def % parameter p
+%/p 3 def
+/n \psk@pstCoxeter@dimension\space def% dimension
+/n_1 n 1 sub def % n-1
+/p_1 p 1 sub def % p-1
+1 setlinejoin CLW setlinewidth%
+%
+%
+% The procedures
+%
+% /drawEdges : draw the edges of the polytopes
+/drawEdges { /pow2 1 def
+ 1 1 n_1 {/pop %for from 1 to n-1
+ /pow2 pow2 p mul def%
+ } for % compute p^{n-1}
+%
+ 1 1 n {% for i from 1 to n
+ /i exch def
+ 0 1 pow2 1 sub { % for j from 0 to p^{n-1}-1
+ /j exch def
+ /num j def % num := j
+ /s1 0 def % s1 := 0
+ /s2 0 def % s2 := 0
+ 1 1 i 1 sub {% for k from 1 to i-1
+ /k exch def
+ /c unit k n num mul add 2 Pi mul mul p div n div cos mul def% c := cos( (p*num+k)*2*Pi/p/n)*unit
+ /s unit k n num mul add 2 Pi mul mul p div n div sin mul def% s := sin( (p*num+k)*2*Pi/p/n)*unit
+ /s1 s1 c add def %s1 := s1+c
+ /s2 s2 s add def %s2 := s2+s
+ /num num p idiv def % num := num/p
+ } for
+ i 1 add 1 n {% for k from i+1 to n
+ /k exch def
+ /c unit k n num mul add 2 Pi mul mul p div n div cos mul def% c := cos( (p*num+k)*2*Pi/p/n)*unit
+ /s unit k n num mul add 2 Pi mul mul p div n div sin mul def% s := sin( (p*num+k)*2*Pi/p/n)*unit
+ /s1 s1 c add def %s1 := s1+c
+ /s2 s2 s add def %s2 := s2+s
+ /num num p idiv def % num := num/p
+ } for
+ /x unit i 2 Pi mul mul p div n div cos mul s1 add def %x := s1+unit*cos(2*i*Pi/p/n)
+ /y unit i 2 Pi mul mul p div n div sin mul s2 add def %y := s2+unit*sin(2*i*Pi/n)
+ x y moveto %
+ 0 1 p { % from jj from 0 to p
+ /jj exch def
+ /x unit i jj n mul add 2 Pi mul mul n div p div cos mul s1 add def %x := s1+unit*cos((i+jj*n)*Pi*2/p/n)
+ /y unit i jj n mul add 2 Pi mul mul n div p div sin mul s2 add def %y := s2+unit*sin((i+jj*n)*Pi*2/p/n)
+ x y lineto
+ } for
+ stroke
+}for
+ } for
+ stroke
+} def \ifPst@drawedges
+ drawEdges
+ stroke
+\fi
+%
+% \drawVertices : draw the vertices of the polytopes
+%
+% Almost the same procedure than \drawEdges
+/DS \pst@number\pssizeVertices\space def
+\@nameuse{psds@\psk@styleVertices}%
+/drawVertices {%
+ /pow2 1 def
+ 1 1 n_1 {/pop
+ /pow2 pow2 p mul def%
+ } for
+%
+ 1 1 n {%
+ /i exch def
+ 0 1 pow2 1 sub { % for j from 0 to p^{n-1}-1
+ /j exch def
+ /num j def
+ /s1 0 def
+ /s2 0 def
+ 1 1 i 1 sub {% for k from 1 to i-1
+ /k exch def
+ /c unit k n num mul add 2 Pi mul mul p div n div cos mul def% cos( (p*num+k)*2*Pi/p/n)*unit
+ /s unit k n num mul add 2 Pi mul mul p div n div sin mul def% sin( (p*num+k)*2*Pi/p/n)*unit
+ /s1 s1 c add def %s1=s1+c
+ /s2 s2 s add def %s2=s2+s
+ /num num p idiv def % num:=num/p
+ } for
+ i 1 add 1 n {% for k from i+1 to n
+ /k exch def
+ /c unit k n num mul add 2 Pi mul mul p div n div cos mul def% cos( (p*num+k)*2*Pi/p/n)*unit
+ /s unit k n num mul add 2 Pi mul mul p div n div sin mul def% sin( (p*num+k)*2*Pi/p/n)*unit
+ /s1 s1 c add def %s1=s1+c
+ /s2 s2 s add def %s2=s2+s
+ /num num p idiv def % num:=num/p
+ } for
+ /x unit i 2 Pi mul mul p div n div cos mul s1 add def %x:=s1+unit*cos(2*i*Pi/p/n)
+ /y unit i 2 Pi mul mul p div n div sin mul s2 add def
+ pscolorVertices
+ x y
+ Dot
+ 0 1 p { % for jj from 0 to p
+ /jj exch def
+ /x unit i jj n mul add 2 Pi mul mul n div p div cos mul s1 add def%x:=s1+unit*cos((i+jj*n)*Pi*2/p/n)
+ /y unit i jj n mul add 2 Pi mul mul n div p div sin mul s2 add def
+ pscolorVertices
+ x y
+ Dot
+ } for
+ stroke
+}for
+ } for
+ stroke
+} def \ifPst@drawvertices
+ %Tableaaux
+ drawVertices
+\fi
+%
+% \drawCenters : draw the centers of the edges of the polytopes
+%
+% Almost the same procedure than \drawEdges
+/DS \pst@number\pssizeCenters\space def
+\@nameuse{psds@\psk@styleCenters}%
+/drawCenters {
+ /pow2 1 def
+ 1 1 n_1 {/pop
+ /pow2 pow2 p mul def%
+ } for
+%
+ 1 1 n {%
+ /i exch def
+ 0 1 pow2 1 sub { % for j from 0 to p^{n-1}-1
+ /j exch def
+ /num j def
+ /s1 0 def
+ /s2 0 def
+ 1 1 i 1 sub {% for k from 1 to i-1
+ /k exch def
+ /c unit k n num mul add 2 Pi mul mul p div n div cos mul def% cos( (p*num+k)*2*Pi/p/n)*unit
+ /s unit k n num mul add 2 Pi mul mul p div n div sin mul def% sin( (p*num+k)*2*Pi/p/n)*unit
+ /s1 s1 c add def %s1=s1+c
+ /s2 s2 s add def %s2=s2+s
+ /num num p idiv def % num:=num/p
+ } for
+ i 1 add 1 n {% for k from i+1 à n
+ /k exch def
+ /c unit k n num mul add 2 Pi mul mul p div n div cos mul def% cos( (p*num+k)*2*Pi/p/n)*unit
+ /s unit k n num mul add 2 Pi mul mul p div n div sin mul def% sin( (p*num+k)*2*Pi/p/n)*unit
+ /s1 s1 c add def %s1=s1+c
+ /s2 s2 s add def %s2=s2+s
+ /num num p idiv def % num:=num/p
+ } for
+ /x unit i 2 Pi mul mul p div n div cos mul s1 add def %x:=s1+unit*cos(2*i*Pi/p/n)
+ /y unit i 2 Pi mul mul p div n div sin mul s2 add def
+ 1 1 p 1 sub { % for jj from 1 to p-1
+ /jj exch def
+ /x unit i jj n mul add 2 Pi mul mul n div p div cos mul s1 add x add def%x:=s1+unit*cos((i+jj*n)*Pi*2/p/n)
+ /y unit i jj n mul add 2 Pi mul mul n div p div sin mul s2 add y add def
+ } for
+ /x x p 0 add div def
+ /y y p 0 add div def
+ pscolorCenters
+ x y
+ Dot
+ stroke
+}for
+ } for
+ stroke
+ } def
+\ifPst@drawcenters
+ drawCenters
+\fi }
+\end@ClosedObj
+}}
+%
+%%%%%%%%%%%%%%%%%% The polytopes $\beta^p_n$
+% These polytopes are complex polytopes $2\{3\}2\{3\}2\dots 2\{4\}p$ in the notation of Coxeter.
+% They are the reciprocal polytopes of $\gamma^p_n$
+% When $p=2$, the polytope $\beta^2_n$ is an hyperoctaedre.
+% When $n=2$, the projection is not convenient since the projection of some vertices are the same.
+% For an other projection, use the macro \betaptwo described below.
+%
+% The two parameters are the dimension and $p$.
+%
+% Use the macro \betapn[dimension=...,P=...] to draw the projection of a polytope $\beta^p_n$.
+%
+% Example : \betapn[dimension=5,P=4]
+%%
+%
+%
+\def\betapn{\pst@object{betapn}}
+\def\betapn@i{\@ifnextchar[{\betapn@do}{\betapn@do[]}}
+\def\betapn@do[#1]{{%
+\pst@killglue
+\setkeys{psset}{#1}%
+\begin@ClosedObj
+\addto@pscode{%
+% Some useful definitions
+/pscolorVertices {\pst@usecolor\pscolorVertices currentrgbcolor} def
+ /pscolorCenters {\pst@usecolor\pscolorCenters currentrgbcolor} def
+0 0 translate
+/unit \pst@number\psunit\space def % pts -> cm
+/Pi 180 def
+/p \psk@pstCoxeter@P\space def % parameter
+%/p 3 def
+/n \psk@pstCoxeter@dimension\space def% dimension
+/n_1 n 1 sub def % n-1
+/p_1 p 1 sub def % p-1
+1 setlinejoin CLW setlinewidth%
+ /TableauxPoints [
+] def
+%
+%%%%% The procedures
+% % /drawEdges : draw the edges of the polytopes
+ /drawEdges {
+ 0 1 n { % for k from 0 to n
+ /k exch def
+ k 1 add 1 n{ % for l from k+1 to n
+ /l exch def
+ 0 1 p { % for i from 0 to p
+ /i exch def
+ 0 1 p { % for j from 0 to p
+ /j exch def
+ /s1 unit n i mul k add 2 Pi mul mul n div p div cos mul def % s1 := unit*cos(2*Pi*(n*i)+k)/n/p)
+ /s2 unit n i mul k add 2 Pi mul mul n div p div sin mul def % s2 := unit*sin(2*Pi*(n*i)+k)/n/p)
+ /s3 unit n j mul 1 k add add 2 Pi mul mul n div p div cos mul def % s3 := unit*cos(2*Pi*(n*j)+k)/n/p)
+ /s4 unit n j mul 1 k add add 2 Pi mul mul n div p div sin mul def % s4 := unit*sin(2*Pi*(n*j)+k)/n/p)
+ s1 s2 moveto
+ s3 s4 lineto
+ stroke
+ }for
+ }for
+ } for
+ }for
+ } def \ifPst@drawedges
+ drawEdges
+ stroke
+\fi
+%
+% \drawVertices : draw the vertices of the polytopes
+%
+% Almost the same procedure than \drawEdges
+/DS \pst@number\pssizeVertices\space def
+\@nameuse{psds@\psk@styleVertices}%
+/drawVertices {%
+ 0 1 n {
+ /k exch def
+ k 1 add 1 n{
+ /l exch def
+ 0 1 p 0 sub {
+ /i exch def
+ 0 1 p 0 sub {
+ /j exch def
+ /s1 unit n i mul k add 2 Pi mul mul n div p div cos mul def
+ /s2 unit n i mul k add 2 Pi mul mul n div p div sin mul def
+ /s3 unit n j mul 1 k add add 2 Pi mul mul n div p div cos mul def
+ /s4 unit n j mul 1 k add add 2 Pi mul mul n div p div sin mul def
+ pscolorVertices
+ s1 s2 %radiusVertices 0 360 arc
+ Dot
+ %0 1 0 setrgbcolor % green
+ %pscolorVertices
+ % fill
+ s3 s4 %radiusVertices 0 360 arc
+ Dot
+ %0 1 0 setrgbcolor % green
+ %pscolorVertices
+ %fill
+ stroke
+ }for
+ }for
+ } for
+ }for
+} def \ifPst@drawvertices
+ drawVertices
+\fi
+%
+% \drawCenters : draw the vertices of the polytopes
+%
+% Almost the same procedure than \drawCenters
+/DS \pst@number\pssizeCenters\space def
+\@nameuse{psds@\psk@styleCenters}%
+/drawCenters {
+ 0 1 n {
+ /k exch def
+ k 1 add 1 n{
+ /l exch def
+ 0 1 p 0 sub {
+ /i exch def
+ 0 1 p 0 sub {
+ /j exch def
+ /s1 unit n i mul k add 2 Pi mul mul n div p div cos mul def
+ /s2 unit n i mul k add 2 Pi mul mul n div p div sin mul def
+ /s3 unit n j mul 1 k add add 2 Pi mul mul n div p div cos mul def
+ /s4 unit n j mul 1 k add add 2 Pi mul mul n div p div sin mul def
+ pscolorCenters
+ %newpath
+ s1 s3 add 2 div s2 s4 add 2 div %1.5 0 360 arc
+ %closepath
+ Dot
+ %1 0 0 setrgbcolor % red
+ stroke
+ }for
+ }for
+ } for
+ }for
+ } def \ifPst@drawcenters
+ drawCenters
+\fi
+}%
+\end@ClosedObj
+}}
+%
+% %%%%% Polygon $\gamma^p_2$
+% A special projection for polytopes $\gamma^p_2$.
+%
+\def\gammaptwo{\pst@object{gammaptwo}}
+\def\gammaptwo@i{\@ifnextchar[{\gammaptwo@do}{\gammaptwo@do[]}}
+\def\gammaptwo@do[#1]{{%
+\pst@killglue
+\setkeys{psset}{#1}%
+\begin@ClosedObj
+\addto@pscode{%
+/pscolorVertices {\pst@usecolor\pscolorVertices currentrgbcolor} def
+ /pscolorCenters {\pst@usecolor\pscolorCenters currentrgbcolor} def
+0 0 translate
+/unit \pst@number\psunit\space def % pts -> cm
+/Pi 180 def
+/p \psk@pstCoxeter@P\space def % parameter
+/p_1 p 1 add def % p+1
+1 setlinejoin CLW setlinewidth
+% list of the vertices
+/TableauxPointsL [
+0 1 p_1 {% for n from 0 to p-1
+ /n exch def
+0 1 p { % for n from 0 to p
+ /i exch def
+ [
+ 2 n Pi mul mul p div cos 7.5 sin mul % cos(2nPi/p)sin(Pi/24)
+ 2 n Pi mul mul p div sin 7.5 cos mul add % +sin(2nPi/p)cos(Pi/24)
+ 2 i Pi mul mul p div cos 7.5 sin mul sub % -cos(2iPi/p)sin(Pi/24)
+ 2 i Pi mul mul p div sin 7.5 cos mul sub % -sin(2iPi/p)cos(Pi/24)
+ %
+ unit mul % pts to cm
+ 2 n Pi mul mul p div cos 7.5 cos mul % cos(2nPi/p)cos(Pi/24)
+ 2 n Pi mul mul p div sin 7.5 sin mul sub % -sin(2nPi/p)sin(Pi/24)
+ 2 i Pi mul mul p div cos 7.5 cos mul add % +cos(2iPi/p)cos(Pi/24)
+ 2 i Pi mul mul p div sin 7.5 sin mul sub % -sin(2iPi/p)sin(Pi/24)
+ unit mul % pts to cm
+ ]
+ } for
+ } for
+] def
+%
+/TableauxPointsR [
+0 1 p_1 {%for n from 0 to p-1
+ /n exch def
+0 1 p {% for i from 0 to p
+ /i exch def
+ [
+ 2 i Pi mul mul p div cos 7.5 sin mul % cos(2iPi/p)sin(Pi/24)
+ 2 i Pi mul mul p div sin 7.5 cos mul add % +sin(2iPi/p)cos(Pi/24)
+ 2 n Pi mul mul p div cos 7.5 sin mul sub % -cos(2nPi/p)sin(Pi/24)
+ 2 n Pi mul mul p div sin 7.5 cos mul sub % -sin(2nPi/p)cos(Pi/24)
+ unit mul % pts to cm
+ %
+ 2 i Pi mul mul p div cos 7.5 cos mul % cos(2iPi/p)cos(Pi/24)
+ 2 i Pi mul mul p div sin 7.5 sin mul sub % -sin(2iPi/p)sin(Pi/24)
+ 2 n Pi mul mul p div cos 7.5 cos mul add % +cos(2nPi/p)cos(Pi/24)
+ 2 n Pi mul mul p div sin 7.5 sin mul sub % -sin(2nPi/p)sin(Pi/24)
+ unit mul % pts to cm
+ ]
+ } for
+ } for
+] def
+ %%%% The procedures
+ %
+ % / drawEdges draw the edges of the polygon
+/drawEdges {
+ /Liste exch def
+newpath
+ Liste 0 get aload pop moveto
+ 0 1 p_1 p mul {
+ /compteur exch def
+ Liste compteur get aload pop
+ lineto } for
+closepath stroke } def \ifPst@drawedges
+ TableauxPointsL drawEdges
+ TableauxPointsR drawEdges
+\fi
+%
+ % / drawVertices draw the vertices of the polygon
+/DS \pst@number\pssizeVertices\space def
+\@nameuse{psds@\psk@styleVertices}%
+/drawVertices {%
+ /Liste exch def
+ 0 1 p_1 p mul {
+ /compteur exch def
+ pscolorVertices
+ Liste compteur get aload pop
+ Dot
+ pscolorVertices
+ fill
+ } for
+} def \ifPst@drawvertices
+ TableauxPointsL drawVertices
+ TableauxPointsR drawVertices
+\fi
+ %% List of the centers
+/TableauMilieuxL[
+0 1 p 1 sub {% for n from 0 to p-1
+ /n exch def
+ [
+ 2 n Pi mul mul p div cos 7.5 sin mul % cos(2nPi/p)sin(Pi/24)
+ 2 n Pi mul mul p div sin 7.5 cos mul add % +sin(2nPi/p)cos(Pi/24)
+ unit mul % pts to cm
+ 2 n Pi mul mul p div cos 7.5 cos mul % cos(2nPi/p)cos(Pi/24)
+ 2 n Pi mul mul p div sin 7.5 sin mul sub % -sin(2nPi/p)sin(Pi/24)
+ unit mul % pts to cm
+ ]
+ } for
+] def
+%
+/TableauMilieuxR[
+0 1 p 1 sub {% for n from 0 to p-1
+ /n exch def
+ [
+ 2 n Pi mul mul p div cos 7.5 sin mul neg % -cos(2nPi/p)sin(Pi/24)
+ 2 n Pi mul mul p div sin 7.5 cos mul sub % -sin(2nPi/p)cos(Pi/24)
+ unit mul % pts to cm
+ 2 n Pi mul mul p div cos 7.5 cos mul % cos(2nPi/p)cos(Pi/24)
+ 2 n Pi mul mul p div sin 7.5 sin mul sub % -sin(2nPi/p)sin(Pi/24)
+ unit mul % pts to cm
+ ]
+ } for
+] def
+%
+ % / drawEdges draw the edges of the polygon
+/DS \pst@number\pssizeCenters\space def
+\@nameuse{psds@\psk@styleCenters}%
+/drawCenters {%
+ /Liste exch def
+ 0 1 p 1 sub {%
+ /compteur exch def
+ pscolorCenters
+ Liste compteur get aload pop
+ Dot
+ stroke
+ } for
+} def \ifPst@drawcenters
+ TableauMilieuxL drawCenters
+ TableauMilieuxR drawCenters
+\fi
+}%
+\end@ClosedObj
+}}
+%
+%
+% %%%%% Polygon $\gamma^p_2$
+% A special projection for polytopes $\gamma^p_2$.
+%
+%
+\def\betaptwo{\pst@object{betaptwo}}
+\def\betaptwo@i{\@ifnextchar[{\betaptwo@do}{\betaptwo@do[]}}
+\def\betaptwo@do[#1]{{%
+\pst@killglue
+\setkeys{psset}{#1}%
+\begin@ClosedObj
+\addto@pscode{%
+/pscolorVertices {\pst@usecolor\pscolorVertices currentrgbcolor} def
+ /pscolorCenters {\pst@usecolor\pscolorCenters currentrgbcolor} def
+0 0 translate
+/unit \pst@number\psunit\space def % pts -> cm
+/Pi 180 def
+/p \psk@pstCoxeter@P\space def % parameter
+/p_1 p 1 sub def % p-1
+1 setlinejoin CLW setlinewidth
+% List of the vertices
+ /TableauxPointsL24p [
+0 1 p_1 {% for n from 0 to p-1
+ /n exch def
+ [
+ 2 n Pi mul mul p div cos 7.5 sin mul % cos(2nPi/p)sin(Pi/24)
+ 2 n Pi mul mul p div sin 7.5 cos mul add % +sin(2nPi/p)cos(Pi/24)
+ unit mul % pts to cm
+ 2 n Pi mul mul p div cos 7.5 cos mul % cos(2nPi/p)cos(Pi/24)
+ 2 n Pi mul mul p div sin 7.5 sin mul sub % -sin(2nPi/p)cos(Pi/24)
+ unit mul % pts to cm
+ ]
+ } for
+] def
+%
+/TableauxPointsR24p [
+0 1 p_1 {% for m from 0 to p-1
+ /m exch def
+ [
+ 2 m Pi mul mul p div cos 7.5 sin mul neg % cos(2mPi/p)sin(Pi/24)
+ 2 m Pi mul mul p div sin 7.5 cos mul sub % -sin(2mPi/p)cos(Pi/24)
+ unit mul % pts to cm
+ 2 m Pi mul mul p div cos 7.5 cos mul % cos(2mPi/p)cos(Pi/24)
+ 2 m Pi mul mul p div sin 7.5 sin mul sub % -sin(2mPi/p)sin(Pi/24)
+ unit mul % pts to cm
+ ]
+ } for
+] def
+%%%% The procedures
+ %
+ % / drawEdges draw the edges of the polygon
+/drawEdges { 0 1 p_1 { %
+ /n exch def
+ TableauxPointsL24p n get aload pop
+ /YL ED /XL ED
+0 1 p_1 {
+ /m ED
+ XL YL moveto
+ TableauxPointsR24p m get aload pop
+ lineto
+% 0 0 1 setrgbcolor
+ stroke
+ } for } for
+} def
+ \ifPst@drawedges
+ drawEdges
+ stroke
+\fi
+ % / drawVertices draw the vertices of the polygon
+ /DS \pst@number\pssizeVertices\space def
+\@nameuse{psds@\psk@styleVertices}%
+/drawVertices {%
+ /Liste exch def
+ 0 1 p_1 {
+ /compteur exch def
+ % newpath
+ pscolorVertices
+ Liste compteur get aload pop
+ Dot% radiusVertices 0 360 arc
+ %closepath
+%0 1 0 setrgbcolor % green
+%pscolorVertices
+% fill
+ } for
+} def
+%
+\ifPst@drawvertices
+ TableauxPointsL24p drawVertices
+ TableauxPointsR24p drawVertices
+\fi
+ % / drawCenters draw the centers of the edges of the polygon
+/DS \pst@number\pssizeCenters\space def
+\@nameuse{psds@\psk@styleCenters}%
+/drawCenters {
+ 0 1 p_1 {
+ /n exch def
+ TableauxPointsL24p n get aload pop
+ /YL ED /XL ED
+0 1 p_1 {
+ /m ED
+ TableauxPointsR24p m get aload pop
+ /YR ED /XR ED
+ /YM YL YR add 2 div def
+ /XM XL XR add 2 div def
+ pscolorCenters
+ %newpath
+ XM YM %1.5 0 360 arc
+ Dot
+ %closepath
+ %1 0 0 setrgbcolor % red
+ stroke
+ } for } for
+ } def
+\ifPst@drawcenters
+ drawCenters
+\fi }
+\end@ClosedObj
+}}
+%
+%
+%\catcode`\@=\PstAtCode\relax
+\endinput
+%
+%%
+%% END: pst-coxeter.tex
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-04 12:04:16 +0000