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diff --git a/Master/texmf-dist/doc/generic/pst-cox/README b/Master/texmf-dist/doc/generic/pst-cox/README new file mode 100644 index 00000000000..f7622032c22 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-cox/README @@ -0,0 +1,54 @@ +PST-Cox v1.0 +------------------------ +This project contains two LaTeX packages for drawing regular complex polytopes: + - pst-coxcoor: pre-calculated regular polytopes up to dimension 4. + - pst-coxeterp: infinite series of regular complex regular polytopes. + +See for more information the files pst-coxcoor_doc.ps and pst-coxeterp_doc.ps of the package. + +First check whether the project can be installed by the distribution that you use. The packages need PSTrick and xkeyval of Hendri Adriaens. + +The structure and location in the Tex-tree is shown below. + +README.txt: should be not installed + + +| - pst-coxeterp_doc.ps +| --- pst-coxeterp-| +|-doc-| - Gallery_doc.ps +| | +| | - pst-coxcoor_doc.ps +| --- pst-coxcoor-| +| - Gallery.ps +| +| +|-dvips-[-- pst-coxcoor-[ pst-coxeter.pro +| +| +| --- pst-coxeterp-[ pst-coxeterp.sty +| | +| |-latex-| +| | | +| | --- pst-coxcoor-[ pst-coxcoor.sty +|-tex-| +| | --- pst-coxeterp-[ pst_coxeterp.tex +| | | +| |-generic-| +| | | +| | --- pst-coxcoor-[ pst-coxcoor.tex + +Don't forget to update your filename database after installing the +files. + +Contact informations +Jean-Gabriel Luque +Institut Gaspard Monge +Université Paris-Est +77454 Marne-la-Vallée Cedex 2 +Jean-Gabriel.Luque@univ-mlv.fr +or +Jean-Gabriel.Luque@wanadoo.fr + +License +Copyright © 2008 Jean-Gabriel Luque, Manuel Luque. +This work may be distributed and/or modified under the condition of the Lesser GPL. diff --git a/Master/texmf-dist/doc/generic/pst-cox/gpl.txt b/Master/texmf-dist/doc/generic/pst-cox/gpl.txt new file mode 100644 index 00000000000..94a9ed024d3 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-cox/gpl.txt @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/> + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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Luque +% Purpose: Demonstration of the library pst-coxcoor +% 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/>. +% + +\documentclass[a4paper]{article} +\usepackage[latin1]{inputenc}% +\usepackage[margin=2cm]{geometry} +\usepackage{pst-coxcoor} +\usepackage{multido} +\usepackage{graphics} +\newcount\ChoicePolytope + +\def\Titre#1{ +\ifcase\ichoice\or \def\polname{$2\{3\}3$}\def\ep{0.5mm} + \or \def\polname{$3\{3\}2$}\def\ep{0.3mm}\or +\def\polname{$3\{3\}3$}\def\ep{0.3mm}\or + \def\polname{$3\{4\}2$}\def\ep{0.3mm}\or \def\polname{$3\{4\}4$}\def\ep{0.1mm} + \or \def\polname{$3\{4\}3$}\def\ep{0.1mm}\or \def\polname{$4\{3\}4$}\def\ep{0.1mm}\or +\def\polname{$2\{4\}3\{3\}3$}\def\ep{0.1mm}\or \def\polname{ Hessien}\def\ep{0.1mm} + \or \def\polname{$3\{3\}3\{4\}2$}\def\ep{0.1mm} + \or \def\polname{de Witting} \def\ep{0.01mm} \or + \def\polname{$3\{8\}2$} \def\ep{0.1mm} \or + \def\polname{$2\{8\}3$} \def\ep{0.1mm} \or + \def\polname{$3\{5\}3$} \def\ep{0.1mm} + \or\def\polname{$4\{4\}3$} \def\ep{0.1mm} + \or\def\polname{$4\{3\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{3\}4$} \def\ep{0.1mm} + \or\def\polname{$2\{6\}4$} \def\ep{0.1mm} + \or\def\polname{$4\{6\}2$} \def\ep{0.1mm} + \or\def\polname{$5\{3\}5$} \def\ep{0.1mm} + \or\def\polname{$2\{10\}3$} \def\ep{0.1mm} + \or\def\polname{$3\{10\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{5\}3$} \def\ep{0.1mm} + \or\def\polname{$3\{5\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{4\}3$} \def\ep{0.1mm} + \or\def\polname{$2\{3\}2\{4\}3$} \def\ep{0.1mm} + \or\def\polname{$3\{4\}2\{3\}2$} \def\ep{0.1mm} + \or\def\polname{$3\{4\}2\{3\}2\{3\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{3\}2\{3\}2\{4\}3$} \def\ep{0.1mm} + \or\def\polname{$2\{3\}2\{5\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{5\}2\{3\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{3\}2\{3\}2\{4\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{4\}2\{3\}2\{3\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{3\}2\{4\}2\{3\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{3\}2\{3\}2\{5\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{5\}2\{3\}2\{2\}2$} \def\ep{0.1mm} + \or\def\polname{$3\left\{5\over2\right\}3$} \def\ep{0.1mm} + \or\def\polname{$5\left\{5\over2\right\}5$} \def\ep{0.1mm} + \or\def\polname{$2\left\{5\over2\right\}3$} \def\ep{0.1mm} + \or\def\polname{$3\left\{5\over2\right\}2$} \def\ep{0.1mm} + \or\def\polname{$3\left\{10\over3\right\}2$} \def\ep{0.1mm} + \or\def\polname{$2\left\{10\over3\right\}3$} \def\ep{0.1mm} + \or\def\polname{$3\left\{8\over3\right\}2$} \def\ep{0.1mm} + \or\def\polname{$2\left\{8\over3\right\}3$} \def\ep{0.1mm} + \or\def\polname{$5\{6\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{6\}5$} \def\ep{0.1mm} + \or\def\polname{$4\left\{8\over3\right\}3$} \def\ep{0.1mm} + \or\def\polname{$3\left\{8\over3\right\}4$} \def\ep{0.1mm} + \or\def\polname{$5\{5\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{5\}5$} \def\ep{0.1mm} + \or\def\polname{$5\left\{10\over3\right\}2$} \def\ep{0.1mm} + \or\def\polname{$2\left\{10\over3\right\}5$} \def\ep{0.1mm} + \or\def\polname{$5\{3\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{3\}5$} \def\ep{0.1mm} + \or\def\polname{$5\{4\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{4\}5$} \def\ep{0.1mm} + \or\def\polname{$5\left\{10\over3\right\}3$} \def\ep{0.1mm} + \or\def\polname{$3\left\{10\over3\right\}5$} \def\ep{0.1mm} + \or\def\polname{$5\{4\}3$} \def\ep{0.1mm} + \or\def\polname{$3\{4\}5$} \def\ep{0.1mm} + \or\def\polname{$5\{3\}3$} \def\ep{0.1mm} + \or\def\polname{$3\{3\}5$} \def\ep{0.1mm} + \or\def\polname{$5\left\{5\over2\right\}3$} \def\ep{0.1mm} + \or\def\polname{$3\left\{5\over2\right\}5$} \def\ep{0.1mm} + \or\def\polname{$2\left\{5\over2\right\}2\{3\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{3\}2\left\{5\over 2\right\}2$} \def\ep{0.1mm} + \or\def\polname{$2\left\{5\over2\right\}2\{5\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{5\}2\left\{5\over 2\right\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{6\}3$} \def\ep{0.1mm} + \or\def\polname{$3\{6\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{\frac52\}2\{3\}2\{3\}2$} \def\ep{0.1mm} + \fi + {\Huge Polytope \polname} +} +\def\demoPolytopes#1{%} +\begin{center} +\Titre{#1} +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=#1,linewidth=\ep] % par défaut choice=1 (332) +\end{pspicture} + +$\backslash$\texttt{CoxeterCoordinates[choice=#1]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawvertices=false,choice=#1,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawcenters=false,choice=#1,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawedges=false,choice=#1,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=#1]} +& +\texttt{[drawcenters=false,choice=#1]} +& +\texttt{[drawedges=false,choice=#1]} +\end{tabular} +\end{center}} + +\def\demoPolytopesGrand#1{%} +\begin{center} +\Titre{#1} +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=#1,linewidth=\ep] % par défaut choice=1 (332) +\end{pspicture} + +$\backslash$\texttt{CoxeterCoordinates[choice=#1]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=2cm} +\CoxeterCoordinates[drawvertices=false,choice=#1,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=2cm} +\CoxeterCoordinates[drawcenters=false,choice=#1,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=2cm} +\CoxeterCoordinates[drawedges=false,choice=#1,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=#1]} & +\texttt{[drawcenters=false,choice=#1]} & +\texttt{[drawedges=false,choice=#1]} +\end{tabular} +\end{center}} + +% +\def\demoPolytopesPetit#1{%} +\begin{center} +\Titre{#1} +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=#1,linewidth=\ep] % par défaut choice=1 (332) +\end{pspicture} + +$\backslash$\texttt{CoxeterCoordinates[choice=#1]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.2cm} +\CoxeterCoordinates[drawvertices=false,choice=#1,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.2cm} +\CoxeterCoordinates[drawcenters=false,choice=#1,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.2cm} +\CoxeterCoordinates[drawedges=false,choice=#1,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=#1]} & +\texttt{[drawcenters=false,choice=#1]} & +\texttt{[drawedges=false,choice=#1]} +\end{tabular} +\end{center}} + +\title{The Gallery} +\author{Jean-Gabriel \textsc{Luque}\footnote{Jean-Gabriel.Luque@univ-mlv.fr} and Manuel + \textsc{Luque}\footnote{mluque5130@aol.com}} +\begin{document} +\maketitle\newpage +\section{Les polygons (dimension 2)} +\multido{\ichoice=1+1}{7}{% +\demoPolytopes{\ichoice}\newpage} +\begin{center} +{\huge Polytope $3\{8\}2$} +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=12,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=12]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.4cm} +\CoxeterCoordinates[drawvertices=false,choice=12,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.4cm} +\CoxeterCoordinates[drawcenters=false,choice=12,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.4cm} +\CoxeterCoordinates[drawedges=false,choice=12,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=12]} & +\texttt{[drawcenters=false,choice=12]} & +\texttt{[drawedges=false,choice=12]} +\end{tabular} +\end{center}\newpage + +\begin{center} +{\huge Polytope $2\{8\}3$} +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=13,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=13]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.4cm} +\CoxeterCoordinates[drawvertices=false,choice=13,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.4cm} +\CoxeterCoordinates[drawcenters=false,choice=13,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.4cm} +\CoxeterCoordinates[drawedges=false,choice=13,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=13]} & +\texttt{[drawcenters=false,choice=13]} & +\texttt{[drawedges=false,choice=13]} +\end{tabular} +\end{center}\newpage + + +\multido{\ichoice=14+1}{11}{% +\demoPolytopes{\ichoice}\newpage} + +\begin{center} +{\huge Polytope $2\{5\}3$} +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=23,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=23]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm} +\CoxeterCoordinates[drawvertices=false,choice=23,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm} +\CoxeterCoordinates[drawcenters=false,choice=23,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm} +\CoxeterCoordinates[drawedges=false,choice=23,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=23]} +& +\texttt{[drawcenters=false,choice=23]} +& +\texttt{[drawedges=false,choice=23]} +\end{tabular} +\end{center} + +\newpage +\multido{\ichoice=24+1}{2}{% +\demoPolytopes{\ichoice}\newpage} %%%%%% + %ù%%%%%% +\begin{center} + {\huge Polytope $3\{\frac 52\}3$} +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=37,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=37]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm} +\CoxeterCoordinates[drawvertices=false,choice=37,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm} +\CoxeterCoordinates[drawcenters=false,choice=37,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm} +\CoxeterCoordinates[drawedges=false,choice=37,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=37]} & +\texttt{[drawcenters=false,choice=37]} & +\texttt{[drawedges=false,choice=37]} +\end{tabular} +\end{center} +%%%%% +\newpage + +\multido{\ichoice=38+1}{13}{% +\demoPolytopes{\ichoice} +\newpage} +\multido{\ichoice=51+1}{3}{ +\begin{center} +\Titre{\ichoice} +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=\ichoice,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=\ichoice]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawvertices=false,choice=\ichoice,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawcenters=false,choice=\ichoice,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawedges=false,choice=\ichoice,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=\ichoice]} & +\texttt{[drawcenters=false,choice=\ichoice]} & +\texttt{[drawedges=false,choice=\ichoice]} +\end{tabular} +\end{center} +\newpage +} +\begin{center} + \multido{\ichoice=54+1}{1}{ +\Titre{\ichoice}} +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=54,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$ +\texttt{CoxeterCoordinates[choice=54]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm} +\CoxeterCoordinates[drawvertices=false,choice=54,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm} +\CoxeterCoordinates[drawcenters=false,choice=54,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm} +\CoxeterCoordinates[drawedges=false,choice=54,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=54]} & +\texttt{[drawcenters=false,choice=54]} & +\texttt{[drawedges=false,choice=54]} +\end{tabular} +\end{center} +\newpage +\multido{\ichoice=55+1}{5}{% +\demoPolytopes{\ichoice} +\newpage} +\multido{\ichoice=60+1}{1}{ +\begin{center} +\Titre{\ichoice} +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=\ichoice,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=\ichoice]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.2cm} +\CoxeterCoordinates[drawvertices=false,choice=\ichoice,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.2cm} +\CoxeterCoordinates[drawcenters=false,choice=\ichoice,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.2cm} +\CoxeterCoordinates[drawedges=false,choice=\ichoice,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=\ichoice]} & +\texttt{[drawcenters=false,choice=\ichoice]} & +\texttt{[drawedges=false,choice=\ichoice]} +\end{tabular} +\end{center} +\newpage} +\multido{\ichoice=61+1}{3}{ +\begin{center} +\Titre{\ichoice} +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=\ichoice,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=\ichoice]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm} +\CoxeterCoordinates[drawvertices=false,choice=\ichoice,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm} +\CoxeterCoordinates[drawcenters=false,choice=\ichoice,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm} +\CoxeterCoordinates[drawedges=false,choice=\ichoice,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=\ichoice]} & +\texttt{[drawcenters=false,choice=\ichoice]} & +\texttt{[drawedges=false,choice=\ichoice]} +\end{tabular} +\end{center} +\newpage +} +\begin{center} + \multido{\ichoice=64+1}{1}{ +\Titre{\ichoice}} +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=64,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$ \texttt{CoxeterCoordinates[choice=64]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} +\CoxeterCoordinates[drawvertices=false,choice=64,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} +\CoxeterCoordinates[drawcenters=false,choice=64,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} +\CoxeterCoordinates[drawedges=false,choice=64,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=64]} & +\texttt{[drawcenters=false,choice=64]} & +\texttt{[drawedges=false,choice=64]} +\end{tabular} +\end{center} +\newpage + +\section{Polyhedron (dimension 3)} +\multido{\ichoice=8+1}{3}{% +\demoPolytopes{\ichoice} \begin{center} +\begin{pspicture}(-2,-5)(2,5) +\psset{unit=2} +\CoxeterCoordinates[drawvertices=false,drawcentersfaces=true,drawcenters=false,choice=\ichoice,linewidth=0.3mm] +\end{pspicture} +{\tt +[drawvertices=false,drawcentersfaces=true,drawcenters=false,choice=\ichoice,linewidth=0.3mm] +} +\end{center} +\newpage} +\multido{\ichoice=26+1}{2}{% +\demoPolytopes{\ichoice} \begin{center} +\begin{pspicture}(-2,-5)(2,5) +\psset{unit=2} +\CoxeterCoordinates[drawvertices=false,drawcentersfaces=true,drawcenters=false,choice=\ichoice,linewidth=0.3mm] +\end{pspicture} +{\tt +[drawvertices=false,drawcentersfaces=true,drawcenters=false,choice=\ichoice,linewidth=0.3mm] +} +\end{center} +\newpage} + +\multido{\ichoice=30+1}{2}{% +\demoPolytopes{\ichoice} \begin{center} +\begin{pspicture}(-2,-5)(2,5) +\psset{unit=2} +\CoxeterCoordinates[drawvertices=false,drawcentersfaces=true,drawcenters=false,choice=\ichoice,linewidth=0.3mm] +\end{pspicture} +{\tt +[drawvertices=false,drawcentersfaces=true,drawcenters=false,choice=\ichoice,linewidth=0.3mm] +} +\end{center} +\newpage} +\multido{\ichoice=65+1}{4}{% +\demoPolytopesGrand{\ichoice} \begin{center} +\begin{pspicture}(-2,-5)(2,5) +\psset{unit=3} +\CoxeterCoordinates[drawvertices=false,drawcentersfaces=true,drawcenters=false,choice=\ichoice,linewidth=0.3mm] +\end{pspicture} +{\tt +[drawvertices=false,drawcentersfaces=true,drawcenters=false,choice=\ichoice,linewidth=0.3mm] +} +\end{center} +\newpage} + +\section{Polytopes (dimension $4$)} + +\begin{center} +{\Huge Witting polytope}\\ +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=11,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=11]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawvertices=false,choice=11,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawcenters=false,choice=11,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawedges=false,choice=11,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=11]} & +\texttt{[drawcenters=false,choice=11]} & +\texttt{[drawedges=false,choice=11]} +\end{tabular} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1.4cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=11,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=11]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1.4cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=11,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=11]} +\end{center}\newpage +\begin{center} +{\huge Polytope $3\{4\}2\{3\}2\{3\}2$} +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=28,linewidth=0.1mm] % par défaut choice=1 (332) +\end{pspicture} + +$\backslash$\texttt{CoxeterCoordinates[choice=28]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm} +\CoxeterCoordinates[drawvertices=false,choice=28,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm} +\CoxeterCoordinates[drawcenters=false,choice=28,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm} +\CoxeterCoordinates[drawedges=false,choice=28,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=28]} +& +\texttt{[drawcenters=false,choice=28]} +& +\texttt{[drawedges=false,choice=28]} +\end{tabular} +\end{center} +\newpage +\multido{\ichoice=29+1}{1}{% +\demoPolytopes{\ichoice} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1.4cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=\ichoice,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=\ichoice]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1.4cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=\ichoice,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=\ichoice]} +\end{center}\newpage} + +\multido{\ichoice=32+1}{3}{% +\demoPolytopes{\ichoice} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1.4cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=\ichoice,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=\ichoice]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1.4cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=\ichoice,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=\ichoice]} +\end{center}\newpage} +\begin{center} +{\Huge Le $600$-topes}\\ +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=35,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=35]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} +\CoxeterCoordinates[drawvertices=false,choice=35,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} +\CoxeterCoordinates[drawcenters=false,choice=35,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} +\CoxeterCoordinates[drawedges=false,choice=35,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=35]} & +\texttt{[drawcenters=false,choice=35]} & +\texttt{[drawedges=false,choice=35]} +\end{tabular} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1.5cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=35,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=35]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1.5cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=35,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=35]} +\end{center}\newpage + +\begin{center} +{\Huge The $120$-topes}\\ +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=3.5cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=36,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=36]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} +\CoxeterCoordinates[drawvertices=false,choice=36,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} +\CoxeterCoordinates[drawcenters=false,choice=36,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} +\CoxeterCoordinates[drawedges=false,choice=36,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=36]} & +\texttt{[drawcenters=false,choice=36]} & +\texttt{[drawedges=false,choice=36]} +\end{tabular} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=2cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=36,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=36]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=2cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=36,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=36]} +\end{center}\newpage + +%\multido{\ichoice=71+1}{1}{% +%\demoPolytopesPetit{\ichoice} \begin{center} +%\begin{pspicture}(-2,-5)(2,5) +%\psset{unit=0.5} +%\CoxeterCoordinates[drawvertices=false,drawcentersfaces=true,drawcenters=false,choice=\ichoice,linewidth=0.1mm] +%\end{pspicture} +%{\tt +%[drawvertices=false,drawcentersfaces=true,drawcenters=false,choice=\ichoice,linewidth=0.1mm] +%} +%\end{center} +%\newpage} +\begin{center} +{\Huge The great starry $600$-topes}\\ +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=0.9cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=71,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=71]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.2cm} +\CoxeterCoordinates[drawvertices=false,choice=71,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.2cm} +\CoxeterCoordinates[drawcenters=false,choice=71,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.2cm} +\CoxeterCoordinates[drawedges=false,choice=71,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=71]} & +\texttt{[drawcenters=false,choice=71]} & +\texttt{[drawedges=false,choice=71]} +\end{tabular} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=71,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=71]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=71,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=71]} +\end{center}\newpage +% +% +\begin{center} +{\Huge The great starry $120$-topes}\\ +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=6cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=72,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=72]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.5cm} +\CoxeterCoordinates[drawvertices=false,choice=72,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.5cm} +\CoxeterCoordinates[drawcenters=false,choice=72,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.5cm} +\CoxeterCoordinates[drawedges=false,choice=72,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=72]} & +\texttt{[drawcenters=false,choice=72]} & +\texttt{[drawedges=false,choice=72]} +\end{tabular} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=5cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=72,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=72]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=10cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=72,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=72]} +\end{center}\newpage +% +% +% +\begin{center} +{\Huge $2\{3\}2\{\frac52\}2\{5\}2$}\\ +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=73,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=73]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm} +\CoxeterCoordinates[drawvertices=false,choice=73,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm} +\CoxeterCoordinates[drawcenters=false,choice=73,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm} +\CoxeterCoordinates[drawedges=false,choice=73,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=73]} & +\texttt{[drawcenters=false,choice=73]} & +\texttt{[drawedges=false,choice=73]} +\end{tabular} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=2cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=73,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=73]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=2cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=73,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=73]} +\end{center}\newpage +% +% +% +\begin{center} +{\Huge $2\{3\}2\{5\}2\{\frac52\}2$}\\ +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=6cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=74,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=74]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.5cm} +\CoxeterCoordinates[drawvertices=false,choice=74,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.5cm} +\CoxeterCoordinates[drawcenters=false,choice=74,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.5cm} +\CoxeterCoordinates[drawedges=false,choice=74,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=74]} & +\texttt{[drawcenters=false,choice=74]} & +\texttt{[drawedges=false,choice=74]} +\end{tabular} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=3cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=74,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=74]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=3cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=74,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=74]} +\end{center}\newpage +% +% +\begin{center} +{\Huge $2\{\frac52\}2\{3\}2\{5\}2$}\\ +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=75,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=75]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawvertices=false,choice=75,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawcenters=false,choice=75,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawedges=false,choice=75,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=75]} & +\texttt{[drawcenters=false,choice=75]} & +\texttt{[drawedges=false,choice=75]} +\end{tabular} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=2.5cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=75,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=75]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=3cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=75,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=75]} +\end{center}\newpage +% +% +\begin{center} +{\Huge $2\{\frac52\}2\{5\}2\{3\}2$}\\ +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=76,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=76]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawvertices=false,choice=76,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawcenters=false,choice=76,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawedges=false,choice=76,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=76]} & +\texttt{[drawcenters=false,choice=76]} & +\texttt{[drawedges=false,choice=76]} +\end{tabular} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=2.5cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=76,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=76]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=3cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=76,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=76]} +\end{center}\newpage +% +\begin{center} +{\Huge $2\{5\}2\{3\}2\{\frac52\}2$}\\ +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=77,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=77]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawvertices=false,choice=77,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawcenters=false,choice=77,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawedges=false,choice=77,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=77]} & +\texttt{[drawcenters=false,choice=77]} & +\texttt{[drawedges=false,choice=77]} +\end{tabular} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=2.5cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=77,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=77]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=3cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=77,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=77]} +\end{center}\newpage +% +\begin{center} +{\Huge $2\{5\}2\{\frac52\}2\{3\}2$}\\ +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=5cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=78,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=78]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawvertices=false,choice=78,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawcenters=false,choice=78,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawedges=false,choice=78,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=78]} & +\texttt{[drawcenters=false,choice=78]} & +\texttt{[drawedges=false,choice=78]} +\end{tabular} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=2.5cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=78,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=78]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=3cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=78,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=78]} +\end{center}\newpage + +% +\begin{center} +{\Huge $2\{5\}2\{\frac52\}2\{5\}2$}\\ +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=5cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=79,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=79} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawvertices=false,choice=79,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawcenters=false,choice=79,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawedges=false,choice=79,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=79]} & +\texttt{[drawcenters=false,choice=79]} & +\texttt{[drawedges=false,choice=79]} +\end{tabular} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=2.5cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=79,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=79]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=3cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=79,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=79]} +\end{center}\newpage +% +\begin{center} +{\Huge $2\{\frac525\}2\{5\}2\{\frac52\}2$}\\ +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=80,linewidth=0.01mm] % par défaut choice=1 (332) +\end{pspicture} +$\backslash$\texttt{CoxeterCoordinates[choice=80]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.4cm} +\CoxeterCoordinates[drawvertices=false,choice=80,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.4cm} +\CoxeterCoordinates[drawcenters=false,choice=80,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.4cm} +\CoxeterCoordinates[drawedges=false,choice=80,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=80]} & +\texttt{[drawcenters=false,choice=80]} & +\texttt{[drawedges=false,choice=80]} +\end{tabular} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=80,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,drawedges=false,drawcenters=false,drawcentersfaces=true,choice=80]} +\end{center} +\begin{center} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1cm} +\CoxeterCoordinates[drawvertices=false,drawedges=false,drawcenters=false,drawcenterscells=true,choice=80,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawcenters=false,choice=80]} +\end{center}\newpage + + +\section{Examples} +\begin{center} +\begin{pspicture}(-5,-5)(5,5) +\psset{unit=2}%\rotatebox{90}{ +\CoxeterCoordinates[drawcenters=false,drawcentersfaces=true, +choice=8,linewidth=0.3mm,linecolor=green,linecolor=blue,sizeCentersFaces=0.15, +colorCentersFaces=red,styleCentersFaces=pentagon] +%} +% \psset{unit=1} +\CoxeterCoordinates[drawvertices=false,choice=9,linewidth=0.01mm, +styleCenters=+,sizeCenters=0.1,colorCenters=black] +\end{pspicture}\\ +%Les centres des ar\^etes d'un polytope Hessien sont les sommets +%d'un polytope $2\{4\}3\{3\}3$. +The centers of the edges of an Hessian are the vertices of a +$2\{4\}3\{3\}3$. +\begin{verbatim} +\psset{unit=2}%\rotatebox{90}{ +\CoxeterCoordinates[drawcenters=false,drawcentersfaces=true, +choice=8,linewidth=0.3mm,linecolor=green,linecolor=blue,sizeCentersFaces=0.15, +colorCentersFaces=red,styleCentersFaces=pentagon] +%} + \psset{unit=1} +\CoxeterCoordinates[drawvertices=false,choice=9,linewidth=0.01mm, +styleCenters=+,sizeCenters=0.1,colorCenters=black] +\end{verbatim} +\end{center} +\newpage +\begin{center} +\begin{pspicture}(-2,-7)(2,10) +\psset{unit=2} \rotatebox{90}{ +\CoxeterCoordinates[drawcenters=false,choice=10,linewidth=0.3mm,linecolor=green,sizeVertices=0.2, +colorVertices=magenta]} \psset{unit=1.725} +\CoxeterCoordinates[drawvertices=false,choice=9,linewidth=0.01mm, +styleCenters=+,sizeCenters=0.1,colorCenters=black] +\end{pspicture}\\ +%Les centres des ar\^etes d'un polytope Hessien sont les sommets +%d'un polytope $2\{4\}3\{3\}3$. +The centers of the edges of an Hessian are a the vertices of a +$3\{3\}3\{4\}2$. +\begin{verbatim} +\psset{unit=2} \rotatebox{90}{ +\CoxeterCoordinates[drawcenters=false,choice=10,linewidth=0.3mm,linecolor=green,sizeVertices=0.2, +colorVertices=magenta]} \psset{unit=1.725} +\CoxeterCoordinates[drawvertices=false,choice=9,linewidth=0.01mm, +styleCenters=+,sizeCenters=0.1,colorCenters=black]\end{verbatim} +\end{center} +\newpage +\begin{center} +\begin{pspicture}(-2,-7)(2,10) +\psset{unit=3} +\CoxeterCoordinates[drawcenters=false,choice=8,linewidth=1mm,sizeVertices=0.1,colorVertices=magenta] +\psset{unit=1} +\CoxeterCoordinates[drawcenters=false,choice=9,linewidth=0.01mm,linecolor=blue, +styleVertices=triangle,sizeVertices=0.07,colorVertices=blue] +\rotatebox{180} +{\CoxeterCoordinates[drawcenters=false,choice=9,linewidth=0.01mm,linecolor=green, +styleVertices=triangle,sizeVertices=0.07,colorVertices=green]}\end{pspicture}\\ +%Les sommets d'un polytope $2\{4\}3\{3\}3$ sont les sommets de deux +%polytopes Hessien r\'eciproques. +The vertices of a polytope $2\{4\}3\{3\}3$ are the vertices of two +reciprocal Hessien polytopes +\begin{verbatim} +\psset{unit=3} +\CoxeterCoordinates[drawcenters=false,choice=8,linewidth=1mm, +sizeVertices=0.1,colorVertices=magenta] +\psset{unit=1} +\CoxeterCoordinates[drawcenters=false,choice=9,linewidth=0.01mm,linecolor=blue, +styleVertices=+,sizeVertices=0.1,colorVertices=blue] \rotatebox{180} +{\CoxeterCoordinates[drawcenters=false,choice=9,linewidth=0.01mm,linecolor=green, +styleVertices=+,sizeVertices=0.1,colorVertices=green]} +\end{verbatim} +\end{center}\newpage +\begin{center} +\begin{pspicture}(-2,-8)(2,8) +\psset{unit=2} \rotatebox{180} +{\CoxeterCoordinates[drawcenters=false,choice=9, +linewidth=0.3mm,linecolor=green,styleVertices=triangle,sizeVertices=0.1,colorVertices=blue]} +\psset{unit=2} +\CoxeterCoordinates[drawvertices=false,drawcenters=false,drawcentersfaces=true +,choice=9,linewidth=0.01mm] +\end{pspicture}\\ +%Les centres des faces d'un polytope Hessien sont les sommets d'un +%polytope Hessien (r\'eciproque du premier). +The centers of the faces of an Hessian are the vertices of its +reciprocal. +\begin{verbatim} +\psset{unit=2} \rotatebox{180} +{\CoxeterCoordinates[drawcenters=false,choice=9, +linewidth=0.3mm,linecolor=green,styleVertices=triangle,sizeVertices=0.1,colorVertices=blue]} +\psset{unit=2} +\CoxeterCoordinates[drawvertices=false,drawcenters=false,drawcentersfaces=true +,choice=9,linewidth=0.01mm] +\end{verbatim} +\end{center} +\newpage +\begin{center} +\begin{pspicture}(-2,-8)(2,8) +\psset{unit=1.5} \rotatebox{180} +{\CoxeterCoordinates[drawcenters=false,choice=8, +linewidth=0.3mm,linecolor=green,styleVertices=triangle,sizeVertices=0.1,colorVertices=blue]} +\psset{unit=2} +\CoxeterCoordinates[drawvertices=false,drawcenters=false,drawcentersfaces=true +,choice=10,linewidth=0.01mm] +\end{pspicture}\\ +%Les centres des faces d'un polytope $2\{4\}3\{3\}3$ sont les +%sommets d'un polytope $3\{3\}3\{4\}2$ (r\'eciproque du premier). +The centers of the faces of a $2\{4\}3\{3\}3$ are the vertices of a +$3\{3\}3\{4\}2$. +\begin{verbatim} +\psset{unit=1.5} \rotatebox{180} +{\CoxeterCoordinates[drawcenters=false,choice=8, +linewidth=0.3mm,linecolor=green,styleVertices=triangle,sizeVertices=0.1,colorVertices=blue]} +\psset{unit=2} +\CoxeterCoordinates[drawvertices=false,drawcenters=false,drawcentersfaces=true +,choice=10,linewidth=0.01mm] +\end{verbatim} +\end{center} +\newpage +\begin{center} +\begin{pspicture}(-2,-8)(2,8) + \psset{unit=2.5} +\CoxeterCoordinates[drawvertices=false,drawcenters=false,choice=11,linewidth=0.01mm, +linecolor=black] \psset{unit=0.575} \reflectbox +{\CoxeterCoordinates[drawcenters=false,choice=11, +linewidth=0.01mm,linecolor=yellow,styleVertices=triangle,sizeVertices=0.1,colorVertices=blue]} +\psset{unit=1.73} +\CoxeterCoordinates[drawedges=false,drawvertices=false,drawcenters=false, +drawcenterscells=true ,choice=11] +\end{pspicture}\\ +The centers of the cells of a Witting polytope are the vertices of +its reciprocal. +\begin{verbatim} + \psset{unit=2.5} +\CoxeterCoordinates[drawvertices=false,drawcenters=false,choice=11,linewidth=0.01mm, +linecolor=black] \psset{unit=0.575} \reflectbox +{\CoxeterCoordinates[drawcenters=false,choice=11, +linewidth=0.01mm,linecolor=yellow,styleVertices=triangle,sizeVertices=0.1,colorVertices=blue]} +\psset{unit=1.73} +\CoxeterCoordinates[drawedges=false,drawvertices=false,drawcenters=false, +drawcenterscells=true ,choice=11] +\end{verbatim} +\end{center} +\newpage +\begin{center} +\begin{pspicture}(-2,-8)(2,8) +\psset{unit=3} +\CoxeterCoordinates[drawedges=false,drawcenters=false, + choice=10,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.1] +\CoxeterCoordinates[drawvertices=false,drawcenters=false,choice=27] +\end{pspicture}\\ One of the eight $3\{4\}2\{3\}2$ contained in a $3\{3\}3\{4\}2$. +\begin{verbatim} +\psset{unit=3} +\CoxeterCoordinates[drawedges=false,drawcenters=false, + choice=10,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.1] +\CoxeterCoordinates[drawvertices=false,drawcenters=false,choice=27] +\end{verbatim} +\end{center}\newpage +\begin{center} +\begin{pspicture}(-2,-8)(2,8) +\psset{unit=3} +\CoxeterCoordinates[drawedges=false,drawcenters=false, + choice=10,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.1] +\rotatebox{10.5}{\psset{unit=1.75}\CoxeterCoordinates[drawvertices=false,drawcenters=false,choice=26]} +\end{pspicture}\\ One of the $8$ $2\{3\}2\{4\}3$ contained in a $3\{3\}3\{4\}2$. +\begin{verbatim} +\psset{unit=3} +\CoxeterCoordinates[drawedges=false,drawcenters=false, + choice=10,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.1] +\rotatebox{10.5} {\psset{unit=1.75} +\CoxeterCoordinates[drawvertices=false,drawcenters=false,choice=26]} +\end{verbatim} +\end{center} +\newpage +\begin{center} +\begin{pspicture}(-2,-8)(2,8) +\psset{unit=3} \CoxeterCoordinates[drawcenters=false, + choice=32,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,drawcenterscells=true, + sizeCentersCells=0.05,styleCentersCells=o] + \CoxeterCoordinates[drawcenters=false, + choice=33,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,drawcenterscells=true] + \psset{unit=0.25}\CoxeterCoordinates[drawcenters=false, + choice=33,linecolor=blue,linewidth=0.6mm,colorVertices=blue,sizeVertices=0.1,drawcenterscells=true] +\CoxeterCoordinates[drawcenters=false, + choice=32,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,drawcenterscells=true, + sizeCentersCells=0.05,styleCentersCells=o] + \psset{unit=0.25}\CoxeterCoordinates[drawcenters=false, + choice=33,linecolor=blue,linewidth=0.6mm,colorVertices=blue,sizeVertices=0.1,drawcenterscells=true] +\CoxeterCoordinates[drawcenters=false, + choice=32,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,drawcenterscells=true, + sizeCentersCells=0.05,styleCentersCells=o] + \psset{unit=0.25}\CoxeterCoordinates[drawcenters=false, + choice=33,linecolor=blue,linewidth=0.6mm,colorVertices=blue,sizeVertices=0.1,drawcenterscells=true] +\CoxeterCoordinates[drawcenters=false, + choice=32,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,drawcenterscells=true, + sizeCentersCells=0.05,styleCentersCells=o] +\end{pspicture} +\end{center} +A 16-tope in an hypercube in a 16-tope in an hypercube in ... +\begin{verbatim} +\psset{unit=3} \CoxeterCoordinates[drawcenters=false, + choice=32,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,drawcenterscells=true, + sizeCentersCells=0.05,styleCentersCells=o] + \CoxeterCoordinates[drawcenters=false, + choice=33,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,drawcenterscells=true] + \psset{unit=0.25}\CoxeterCoordinates[drawcenters=false, + choice=33,linecolor=blue,linewidth=0.6mm,colorVertices=blue,sizeVertices=0.1,drawcenterscells=true] +\CoxeterCoordinates[drawcenters=false, + choice=32,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,drawcenterscells=true, + sizeCentersCells=0.05,styleCentersCells=o] + \psset{unit=0.25}\CoxeterCoordinates[drawcenters=false, + choice=33,linecolor=blue,linewidth=0.6mm,colorVertices=blue,sizeVertices=0.1,drawcenterscells=true] +\CoxeterCoordinates[drawcenters=false, + choice=32,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,drawcenterscells=true, + sizeCentersCells=0.05,styleCentersCells=o] + \psset{unit=0.25}\CoxeterCoordinates[drawcenters=false, + choice=33,linecolor=blue,linewidth=0.6mm,colorVertices=blue,sizeVertices=0.1,drawcenterscells=true] +\CoxeterCoordinates[drawcenters=false, + choice=32,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,drawcenterscells=true, + sizeCentersCells=0.05,styleCentersCells=o]\end{verbatim} +\newpage +\newpage +\begin{center} +\begin{pspicture}(-2,-4)(2,4) +\psset{unit=2} +\CoxeterCoordinates[drawcenters=false,drawcentersfaces=false,drawvertices=false, + choice=30,linewidth=0.1mm,linecolor=blue] + \CoxeterCoordinates[drawcenters=false, + choice=31,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,linecolor=magenta] + \CoxeterCoordinates[drawcenters=false,drawcentersfaces=true,drawvertices=false, + drawedges=false,choice=30] +\end{pspicture} +\begin{pspicture}(-2,-4)(2,4) +\psset{unit=2} \CoxeterCoordinates[drawcenters=false, + choice=31,linewidth=0.1mm,drawvertices=false,linecolor=magenta] +{\psset{unit=0.635}\CoxeterCoordinates[drawcenters=false,drawcentersfaces=false, + choice=30,linewidth=0.1mm,linecolor=blue,colorVertices=blue,sizeVertices=0.1] + } + \CoxeterCoordinates[drawcenters=false,drawedges=false,drawcentersfaces=true, + choice=31,linewidth=0.1mm,drawvertices=false] +\end{pspicture} + +\end{center} +A dodec\ae dron in an ikos\ae dron and an iko\ae dron in a dodec\ae +dron. +\begin{verbatim} +\begin{pspicture}(-2,-4)(2,4) +\psset{unit=2} +\CoxeterCoordinates[drawcenters=false,drawcentersfaces=false,drawvertices=false, + choice=30,linewidth=0.1mm,linecolor=blue] + \CoxeterCoordinates[drawcenters=false, + choice=31,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,linecolor=magenta] + \CoxeterCoordinates[drawcenters=false,drawcentersfaces=true,drawvertices=false, + drawedges=false,choice=30] +\end{pspicture} +\begin{pspicture}(-2,-4)(2,4) +\psset{unit=2} \CoxeterCoordinates[drawcenters=false, + choice=31,linewidth=0.1mm,drawvertices=false,linecolor=magenta] +{\psset{unit=0.635}\CoxeterCoordinates[drawcenters=false,drawcentersfaces=false, + choice=30,linewidth=0.1mm,linecolor=blue,colorVertices=blue,sizeVertices=0.1] + } + \CoxeterCoordinates[drawcenters=false,drawedges=false,drawcentersfaces=true, + choice=31,linewidth=0.1mm,drawvertices=false] +\end{pspicture} +\end{verbatim} +\newpage +%%%% +\begin{center} +\begin{pspicture}(-7,-7)(7,7) +\psset{unit=5} +\CoxeterCoordinates[drawcenters=false,drawcentersfaces=false,drawvertices=false, + choice=35,linewidth=0.1mm,linecolor=blue] + {\psset{unit=0.86} + \CoxeterCoordinates[drawcenters=false, + choice=36,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,linecolor=red] + } + \CoxeterCoordinates[drawcenters=false,drawcenterscells=true,drawvertices=false, + drawedges=false,choice=35] +\end{pspicture} +\end{center} +A $120$-tope in a $600$-tope. +\begin{verbatim} +\begin{pspicture}(-7,-7)(7,7) +\psset{unit=5} +\CoxeterCoordinates[drawcenters=false,drawcentersfaces=false,drawvertices=false, + choice=35,linewidth=0.1mm,linecolor=blue] + {\psset{unit=0.86} + \CoxeterCoordinates[drawcenters=false, + choice=36,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,linecolor=red] + } + \CoxeterCoordinates[drawcenters=false,drawcenterscells=true,drawvertices=false, + drawedges=false,choice=35] +\end{pspicture} +\end{verbatim} +\newpage +%%%% +\begin{center} +\begin{pspicture}(-7,-7)(7,7) +\psset{unit=5} +\CoxeterCoordinates[drawcenters=false,drawcentersfaces=false,drawvertices=false, + choice=36,linewidth=0.1mm,linecolor=blue] + \CoxeterCoordinates[drawcenters=false, + choice=35,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,linecolor=red] + \CoxeterCoordinates[drawcenters=false,drawcenterscells=true,drawvertices=false, + drawedges=false,choice=36] +\end{pspicture} +\end{center} +A $600$-tope in a $120$-tope. +\begin{verbatim} +\begin{pspicture}(-7,-7)(7,7) +\psset{unit=5} +\CoxeterCoordinates[drawcenters=false,drawcentersfaces=false,drawvertices=false, + choice=36,linewidth=0.1mm,linecolor=blue] + \CoxeterCoordinates[drawcenters=false, + choice=35,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,linecolor=red] + \CoxeterCoordinates[drawcenters=false,drawcenterscells=true,drawvertices=false, + drawedges=false,choice=36] +\end{pspicture} +\end{verbatim} +\newpage +%%%% +%%%% +\begin{center} +\begin{pspicture}(-7,-7)(7,7) +\psset{unit=0.5} \CoxeterCoordinates[drawcenters=false, + choice=71,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,linecolor=magenta] + \rotatebox{4.5}{\psset{unit=6.9}\CoxeterCoordinates[drawcenters=false, +choice=36,styleVertices=*,linewidth=0.1mm,linecolor=blue]} +\end{pspicture} +\end{center} +A starry $120$-tope in a $120$-tope. +\begin{verbatim} +\psset{unit=0.5} \CoxeterCoordinates[drawcenters=false, + choice=71,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,linecolor=magenta] + \rotatebox{4.5}{\psset{unit=6.9}\CoxeterCoordinates[drawcenters=false, +choice=36,styleVertices=*,linewidth= +\end{verbatim} +%%%% +%\begin{center} +%\begin{pspicture}(-7,-7)(7,7) +%{\psset{unit=5} \CoxeterCoordinates[drawcenters=false, +% choice=72,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,linecolor=magenta]} +% \rotatebox{5}{\CoxeterCoordinates[unit=4.98,drawcenters=false, +%choice=35,styleVertices=*,linewidth=0.1mm,linecolor=blue]} +%\end{pspicture} +%\end{center} +%A starry $600$-tope in a $600$-tope. +%\begin{verbatim} +%\begin{pspicture}(-7,-7)(7,7) +%\psset{unit=0.5} \CoxeterCoordinates[drawcenters=false, +% choice=72,linewidth=0.1mm,colorVertices=blue,sizeVertices=0.05,linecolor=magenta] +% \CoxeterCoordinates[unit=7,drawcenters=false, +%choice=35,styleVertices=*,linewidth=0.1mm,linecolor=blue] +%\end{pspicture}\end{verbatim} +\end{document} diff --git a/Master/texmf-dist/doc/generic/pst-cox/pst-coxcoor/pst-coxcoor_doc.pdf b/Master/texmf-dist/doc/generic/pst-cox/pst-coxcoor/pst-coxcoor_doc.pdf Binary files differnew file mode 100644 index 00000000000..4b24fd50775 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-cox/pst-coxcoor/pst-coxcoor_doc.pdf diff --git a/Master/texmf-dist/doc/generic/pst-cox/pst-coxcoor/pst-coxcoor_doc.tex b/Master/texmf-dist/doc/generic/pst-cox/pst-coxcoor/pst-coxcoor_doc.tex new file mode 100644 index 00000000000..f346c7e410a --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-cox/pst-coxcoor/pst-coxcoor_doc.tex @@ -0,0 +1,1118 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% polygonesCoordinate\pst-coxcoor_doc.tex +% 7 Authors: J.-G. Luque and M. Luque +% 8 Purpose: Documentation for pst-coxcoor +% 9 Created: 02/02/2008 +% 10 License: LGPL +% 11 Project: PST-Cox V1.00 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% polygonesCoordinate\Gallery.tex +% Authors: J.-G. Luque and M. Luque +% Purpose: Demonstration of the library pst-coxcoor +% 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/>. +% + +\documentclass[a4paper]{article} +\usepackage[latin1]{inputenc}% +\usepackage[margin=2cm]{geometry} +\usepackage{pst-coxcoor} +\usepackage{multido} +\usepackage{amssymb} +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{graphics} +% d\'emonstration +% JG Luque 12 août 2003 +\newtheorem{example}{Example}[section] +\newcount\ChoicePolytope +\def\C{{\mathbb C}} + +\title{The Library {\tt pst-coxcoor}} +\author{Jean-Gabriel \textsc{Luque}\footnote{Universit\'e Paris-Est, Laboratoire d'informatique +de l'Institut-Gaspard Monge, Jean-Gabriel.Luque@univ-mlv.fr} and +Manuel + \textsc{Luque}\footnote{mluque5130@aol.com}} +\begin{document} +\maketitle + \begin{abstract} + We describe the {\tt LaTex} library {\tt pst-coxcoor} devoted to + draw regular complex polytopes. + \end{abstract} + \section{Introduction} + Inspired by the dissertation of G.C. Shephard \cite{Sh}, Coxeter + toke twenty years to write his most famous book {\em Regular Complex Polytopes} \cite{Cox}. But its + interest for the polytope dates from the beginning of his career as + shown his numerous publications on the subject (reader can refer to + \cite{Reg} or \cite{Kalei}). According to the preface of + \cite{Cox}, the term of complex polytopes is due to D.M.Y. + Sommerville \cite{Som}. A complex polytope may have more than two + vertices on an edge (and in particular the polygons may have more + than two edges at a vertice). It is a finite set of flags of subspaces in $\C^n$ + with certain constraints + which will be not developed here \footnote{For a precise + definition, see \cite{Cox} Ch12}. + In fact, a complex polytope can be generated from one vertice by a finite number of pseudo-reflections. + More precisely, as for the classical solids, it + can be constructed from an arrangement of mirrors, + considering a point in the intersection of all but one the mirrors + and computing the orbit of this point by the pseudo-reflections generated by the mirrors. In the + case of the real polytopes, one uses classical reflections which are + involutions. It is not the case for general complex polytopes, since + a reflection may include a component which is a rotation. +The classification of the complex polytopes is due to G.C. Shephard +\cite{Sh} and is closely related to the classification of the +complex unitary reflection groups \cite{ST}. Many of these groups +are fundamental in geometry. For example, the polytope Hessian is a +$3$-dimensional polytope whose symmetry group is generated by $3$ +pseudo-reflections $s_1$, $s_2$ and $s_3$ verifying +$s_1^3=s_2^3=s_3^3=Id$, $s_1s_2s_1=s_2s_1s_2$, $s_2s_3s_2=s_3s_2s_3$ +and $s_1s_3=s_3s_1$ and which is related to the determination of the +nine inflection points of a cubic curve and the 27 lines in a cubic +plane.\\ +The library described here is a {\tt LaTex} package for drawing two +dimensional projections of regular complex polytopes. The +coordinates of the vertices, edges, faces... of the projections have +been pre-calculated using a formal computer system.\\ +The polytopes considered are exceptional polytopes, for drawing +infinite series use the package {\it pst-coxeterp}.\\ + Note that this package have already been used by one of the author + to illustrate an article \cite{qutrit} in collaboration with E. Briand, + J.-Y. Thibon and F. Verstraete and in his ``{\it habilitation \`a + diriger les recherches}'' \cite{Luque}. +\section{Install {\tt pst-coxcoor}} +The package contains three files: A latex style file {\tt +pst-coxcoor.sty} which call the latex file {\tt pst-coxcoor.tex} +containing the description of the macro {\tt +$\setminus$CoxeterCoordinates} and a data file {\tt pst-coxcoor.pro} +which contains the list of the coordinates of each polytope.\\ The +installation is very simple. It suffices to +copy the files {\tt pst-coxcoor.sty}, {\tt pst-coxcoor.tex} and\\ +{\tt pst-coxcoor.pro} in the appropriate directories. +\begin{example}\rm +The file {\tt pst-coxcoor.sty} may be copy in the directory \\ {\tt +c:/texmf/tex/latex/pst-coxcoor},\\ + the file {\tt pst-coxcoor.tex} in\\ +{\tt c:/texmf/tex/generic/pst-coxcoor}\\ and the file {\tt +pst-coxcoor.pro} in\\ {\tt c:/texmf/tex/dvips/pst-coxcoor}. +\end{example} +To use the package add the code +\begin{verbatim} +\usepackage{pst-coxcoor}} +\end{verbatim} +in the beginning of your LaTex-file. +\begin{example}\rm +\begin{verbatim} +\documentclass[a4paper]{article} +... +\usepackage{pst-coxcoor} +.... +\end{verbatim} +\end{example} +The library needs the packages {\tt PSTrick} and {\tt pst-xkey}. + +\section{Characteristics of the polytopes} + The polytope considered here are two, three or four + ($\C$)-dimensional objects which generalizes the classical platonic + solids. They are constituted of vertices, edges, faces and cells + (four dimensional faces). The package contains only one macro {\tt $\setminus$CoxeterCoordinates} + which draws the vertices, + the edges, the centers of the edges\footnote{In general, for a complex polytope, the edges are + polygonal.}, the centers of the faces and the centers of the cells. + All the coordinates of the polytopes have been pre-computed and + stored in the file {\tt pst-coxcoor.pro}. +\subsection{List of the polytopes} +The parameter {\tt ichoice} contains the number identifying the +polytope. +\begin{example} +\rm Setting {\tt choice=9} makes the macro draw the (3 dimensional) +Hessian polytope which has $27$ vertices, $72$ triangular edges and +$27$ faces. +\[ +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1.5cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=9] % +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-4,-4)(4,4) +\psset{unit=1.5cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=9] % +\end{pspicture} +\end{verbatim} +\end{example} +There is $80$ pre-calculated polytopes in the file {\tt +pst-coxcoor.pro}. Almost all the complex regular polytopes up to the +dimension four have been computed. Only some starry polytopes in +dimension $4$ are not in the list. The following tableau contains +the list of the polytopes with their names in the notation of +Coxeter \cite{Cox}. +\[ +\begin{array}{|c|c|c|} +\hline 2\{3\}3&3\{3\}3&3\{3\}3\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=1] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=2] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=3] % +\end{pspicture}\\\hline +{\tt choice=1}&{\tt choice=2}&{\tt choice=3}\\\hline +\end{array}\] + %%%% +\[ +\begin{array}{|c|c|c|}\hline + 3\{4\}2&3\{4\}4&3\{4\}3\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.8cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=4] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=5] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=6] % +\end{pspicture}\\\hline +{\tt choice=4}&{\tt choice=5}&{\tt choice=6}\\\hline + %%%% +\end{array}\] + %%%% +\[ +\begin{array}{|c|c|c|}\hline +4\{3\}4&2\{4\}3\{3\}3&3\{3\}3\{3\}3\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=7] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.8cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=8] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=9] % +\end{pspicture}\\\hline +{\tt choice=7}&{\tt choice=8}&{\tt choice=9}\\\hline +\end{array} +\] +%%% +\[ +\begin{array}{|c|c|c|}\hline +3\{3\}3\{4\}2&3\{3\}3\{3\}3\{3\}3&3\{8\}2\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=10] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=11,drawcenters=false] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.4cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=12] % +\end{pspicture}\\\hline +{\tt choice=10}&{\tt choice=11}&{\tt choice=12}\\\hline +\end{array} +\] +%%%% +%%%% +\[ +\begin{array}{|c|c|c|}\hline +2\{8\}3&3\{5\}3&4\{4\}3\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.4cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=13] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=14] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=15] % +\end{pspicture}\\\hline +{\tt choice=13}&{\tt choice=14}&{\tt choice=15}\\\hline +\end{array} +\] +%%% +%%% +\[ +\begin{array}{|c|c|c|}\hline +4\{3\}2&2\{3\}4&2\{6\}4\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=16] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=17] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=18] % +\end{pspicture}\\\hline +{\tt choice=16}&{\tt choice=17}&{\tt choice=18}\\\hline +\end{array} +\] +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +4\{6\}2&5\{3\}5&2\{10\}3\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=19] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=20] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=21] % +\end{pspicture}\\\hline +{\tt choice=19}&{\tt choice=20}&{\tt choice=21}\\\hline +\end{array} +\] +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +3\{10\}2&2\{5\}3&3\{5\}2\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=22] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=23] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=24] % +\end{pspicture}\\\hline +{\tt choice=22}&{\tt choice=23}&{\tt choice=24}\\\hline +\end{array} +\] +%%%% +\[ +\begin{array}{|c|c|c|}\hline +2\{4\}3&2\{3\}2\{4\}3&3\{4\}2\{3\}2\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=25] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.8cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=26] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=27] % +\end{pspicture}\\\hline +{\tt choice=25}&{\tt choice=26}&{\tt choice=27}\\\hline +\end{array} +\] +%%%% +\[ +\begin{array}{|c|c|c|}\hline +3\{4\}2\{3\}2\{3\}2&2\{3\}2\{3\}2\{4\}3&2\{3\}2\{5\}2\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=28] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=29] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=30] % +\end{pspicture}\\\hline +{\tt choice=28}&{\tt choice=29}&{\tt choice=30}\\\hline +\end{array} +\] +%%%% +\[ +\begin{array}{|c|c|c|}\hline +2\{5\}2\{3\}2&2\{3\}2\{3\}2\{4\}2&2\{4\}2\{3\}2\{3\}2\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=31] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=32] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=33] % +\end{pspicture}\\\hline +{\tt choice=31}&{\tt choice=32}&{\tt choice=33}\\\hline +\end{array} +\] +%%%% +\[ +\begin{array}{|c|c|c|}\hline +2\{3\}2\{4\}2\{3\}2&2\{3\}2\{3\}2\{5\}2&2\{5\}2\{3\}2\{3\}2\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=34] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=35,drawcenters=false] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=36,drawcenters=false] % +\end{pspicture}\\\hline +{\tt choice=34}&{\tt choice=35}&{\tt choice=36}\\\hline +\end{array} +\] +%%%% +%%%% +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +3\{\frac52\}3&5\{\frac52\}5&2\{\frac52\}3\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=37] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=38] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.8cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=39] % +\end{pspicture}\\\hline +{\tt choice=37}&{\tt choice=38}&{\tt choice=39}\\\hline +\end{array} +\] +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +3\{\frac52\}2&3\{\frac{10}3\}2&2\{\frac{103}\}3\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=40] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.4cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=41] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=42] % +\end{pspicture}\\\hline +{\tt choice=40}&{\tt choice=41}&{\tt choice=42}\\\hline +\end{array} +\] +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +3\{\frac83\}2&2\{\frac83\}3&5\{6\}2\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.1 cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=43] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=44] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=45] % +\end{pspicture}\\\hline +{\tt choice=43}&{\tt choice=44}&{\tt choice=45}\\\hline +\end{array} +\] +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +2\{6\}5&4\{\frac83\}3&3\{\frac83\}4\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=46] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=47] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=48] % +\end{pspicture}\\\hline +{\tt choice=46}&{\tt choice=47}&{\tt choice=48}\\\hline +\end{array} +\] +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +5\{5\}2&2\{5\}5&5\{\frac{10}3\}2\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=49] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=50] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=51] % +\end{pspicture}\\\hline +{\tt choice=49}&{\tt choice=50}&{\tt choice=51}\\\hline +\end{array} +\] +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +2\{\frac{10}3\}5&5\{3\}2&2\{3\}5\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=52] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=53] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=54] % +\end{pspicture}\\\hline +{\tt choice=52}&{\tt choice=53}&{\tt choice=54}\\\hline +\end{array} +\] +%%% +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +5\{4\}2&2\{4\}5&5\{\frac{10}3\}3\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.8cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=55] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=56] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=57] % +\end{pspicture}\\\hline +{\tt choice=55}&{\tt choice=56}&{\tt choice=57}\\\hline +\end{array} +\] +%%%% +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +3\{\frac{10}3\}5&5\{4\}3&3\{4\}5\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=58] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=59] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.25cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=60] % +\end{pspicture}\\\hline +{\tt choice=58}&{\tt choice=59}&{\tt choice=60}\\\hline +\end{array} +\] +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +5\{3\}3&3\{3\}5&5\{\frac52\}3\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=61] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=62] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.6cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=63] % +\end{pspicture}\\\hline +{\tt choice=61}&{\tt choice=62}&{\tt choice=63}\\\hline +\end{array} +\] +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +3\{\frac52\}5&2\{\frac52\}2\{3\}2&2\{3\}2\{\frac52\}2\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=64] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=2cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=65] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=66] % +\end{pspicture}\\\hline +{\tt choice=64}&{\tt choice=65}&{\tt choice=66}\\\hline +\end{array} +\] +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +2\{\frac52\}2\{3\}2&2\{5\}2\{\frac52\}2&2\{6\}3\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=2.5cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=67] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=5cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=68] % +\end{pspicture} + &\begin{pspicture}(-2,-2)(2,2) +\psset{unit=2.5cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=69] % +\end{pspicture}\\\hline +{\tt choice=67}&{\tt choice=68}&{\tt choice=69}\\\hline +\end{array} +\] +%%%%% +\[ +\begin{array}{|c|c|c|}\hline +3\{6\}2&2\{\frac52\}2\{3\}2\{3\}2&2\{3\}2\{3\}2\{\frac52\}2\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.5cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=70] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.17cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=71] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.4cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=72] % +\end{pspicture}\\ + \hline +{\tt choice=70}&{\tt choice=71}&{\tt choice=72}\\\hline +\end{array} +\] +\[ +\begin{array}{|c|c|c|}\hline +2\{3\}2\{\frac52\}2\{5\}2&2\{3\}2\{5\}2\{\frac52\}2&2\{\frac52\}2\{3\}2\{5\}2\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.4cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=73] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=74] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=75] % +\end{pspicture}\\ + \hline +{\tt choice=73}&{\tt choice=74}&{\tt choice=75}\\\hline +\end{array} +\] +% +\[ +\begin{array}{|c|c|c|}\hline +2\{\frac52\}2\{5\}2\{3\}2&2\{5\}2\{3\}2\{\frac52\}2&2\{5\}2\{\frac52\}2\{3\}2\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=76] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=77] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=78] % +\end{pspicture}\\ + \hline +{\tt choice=76}&{\tt choice=77}&{\tt choice=78}\\\hline +\end{array} +\] +\[ +\begin{array}{|c|c|c|}\hline +2\{5\}2\{\frac52\}2\{5\}2&2\{\frac525\}2\{5\}2\{\frac52\}2\\\hline + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=79] % +\end{pspicture}& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.4cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=80] % +\end{pspicture}\\ + \hline +{\tt choice=79}&{\tt choice=80}\\\hline +\end{array} +\] + + + +\subsection{The components of a polytope} + The library {\tt pst-coxcoor.sty} contains a macro for +drawing the vertices, the edges, the centers of the edges, the +centers of the faces and the centers of the cells of many +pre-calculated regular complex polytopes. + +It is possible to choice which components of the polytope will be +drawn. It suffices to use the boolean parameters {\tt drawedges}, +{\tt drawvertices}, {\tt drawcenters}, {\tt drawcentersface}, and +{\tt drawcenterscells}. + + By default the values of the parameters {\tt +drawedges}, {\tt drawvertices}, {\tt drawcenters} are set to {\tt +true} and the values of {\tt drawcentersface} and {\tt +drawcenterscells} are set to {\tt false}. +\begin{example} +\rm By default, the vertices, the edges and the centers of the edges +are drawn but not the centers of the faces and the cells. +\[ +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[choice=28] % +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} + \CoxeterCoordinates[choice=28] +\end{pspicture} +\end{verbatim} +The macro does not draw the edges +\[ +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[choice=28,drawedges=false] % +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} + \CoxeterCoordinates[choice=28,drawedges=false] +\end{pspicture} +\end{verbatim} +or the vertices +\[ +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[choice=28,drawvertices=false] % +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} + \CoxeterCoordinates[choice=28,drawvertices=false] +\end{pspicture} +\end{verbatim} +or the centers of the edges. +\[ +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[choice=28,drawcenters=false] % +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} + \CoxeterCoordinates[choice=28,drawcenters=false] +\end{pspicture} +\end{verbatim} +Furthermore, one can draw the centers of the faces (when the +dimension of the polytope is at least 3) +\[ +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[choice=28,drawvertices=false,drawcenters=false,drawcentersfaces=true] % +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} + \CoxeterCoordinates[choice=28,drawvertices=false,drawcenters=false,drawcentersfaces=true] +\end{pspicture} +\end{verbatim} +and the centers of the cells (when the dimension of the polytope is +at least 4). +\[ +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[choice=28,drawvertices=false,drawcenters=false,drawcenterscells=true] % +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1cm} + \CoxeterCoordinates[choice=28,drawvertices=false,drawcenters=false,drawcenterscells=true] +\end{pspicture} +\end{verbatim} +\end{example} + +\section{Graphical parameters} +It is possible to change the graphical characteristics of a +polytope.\\ +The size of the polytope depends on the parameter {\tt unit}. +\begin{example} +\rm + \[ + \begin{pspicture}(-1,-1)(1,1) +\CoxeterCoordinates[choice=4,unit=0.3cm] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,unit=0.8cm] % +\end{pspicture} + \begin{pspicture}(-4,-4)(4,4) +\CoxeterCoordinates[choice=4,unit=2cm] % +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-1,-1)(1,1) +\CoxeterCoordinates[choice=4,unit=0.3cm] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,unit=0.8cm] % +\end{pspicture} + \begin{pspicture}(-4,-4)(4,4) +\CoxeterCoordinates[choice=4,unit=2cm] % +\end{pspicture} +\end{verbatim} +\end{example} +Classically, one can modify the color and the width of the edges +using the parameter {\tt linecolor} and {\it linewidth}. +\begin{example} +\rm + \[ +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.8,linewidth=0.01,linecolor=red} +\CoxeterCoordinates[choice=4] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,linewidth=0.1] % +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.8,linewidth=0.01,linecolor=red} +\CoxeterCoordinates[choice=4] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,linewidth=0.1] % +\end{pspicture} +\end{verbatim} +\end{example} +The color, the style and the size of the vertices can be modify +using the parameters {\tt colorVertices}, {\tt styleVertices} and +{\tt sizeVertices}. The style of the vertices can be chosen in the +classical dot styles. +\begin{example} +\rm + \[ +\begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,colorVertices=blue,styleVertices=pentagon,sizeVertices=0.2] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,colorVertices=magenta,sizeVertices=0.1,styleVertices=triangle] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,colorVertices=red,styleVertices=+,sizeVertices=0.2] % +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,colorVertices=blue,styleVertices=pentagon,sizeVertices=0.2] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,colorVertices=magenta,sizeVertices=0.1,styleVertices=triangle] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,colorVertices=red,styleVertices=+,sizeVertices=0.2] % +\end{pspicture} +\end{verbatim} +\end{example} +The color, the style and the size of the centers of the edges can be +modify using the parameters {\tt colorCenters}, {\tt styleCenters} +and {\tt sizeCenters}. +\begin{example} +\rm + \[ +\begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,colorCenters=blue,styleCenters=pentagon,sizeCenters=0.2] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,colorCenters=magenta,sizeCenters=0.1,styleCenters=triangle] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,colorCenters=red,styleCenters=+,sizeCenters=0.2] % +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,colorCenters=blue,styleCenters=pentagon,sizeCenters=0.2] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,colorCenters=magenta,sizeCenters=0.1,styleCenters=triangle] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\CoxeterCoordinates[choice=4,colorCenters=red,styleCenters=+,sizeCenters=0.2] % +\end{pspicture} +\end{verbatim} +\end{example} + +The color, the style and the size of the centers of the faces can be +modify using the parameters {\tt colorCentersFaces}, {\tt +styleCentersFaces} and {\tt sizeCentersFaces}. +\begin{example} +\rm + \[\psset{unit=0.8cm,drawcentersfaces=true} +\begin{pspicture}(-3,-3)(3,3) +\CoxeterCoordinates[choice=33,styleCentersFaces=pentagon,sizeCentersFaces=0.2] % +\end{pspicture} + \begin{pspicture}(-3,-3)(3,3) +\CoxeterCoordinates[choice=33,colorCentersFaces=magenta,sizeCentersFaces=0.1] % +\end{pspicture} + \begin{pspicture}(-3,-3)(3,3) +\CoxeterCoordinates[choice=33,colorCentersFaces=red,styleCentersFaces=+] % +\end{pspicture} +\] +\begin{verbatim} +\psset{unit=0.8cm,drawcentersfaces=true} +\begin{pspicture}(-3,-3)(3,3) +\CoxeterCoordinates[choice=33,styleCentersFaces=pentagon,sizeCentersFaces=0.2] % +\end{pspicture} + \begin{pspicture}(-3,-3)(3,3) +\CoxeterCoordinates[choice=33,colorCentersFaces=magenta,sizeCentersFaces=0.1] % +\end{pspicture} + \begin{pspicture}(-3,-3)(3,3) +\CoxeterCoordinates[choice=33,colorCentersFaces=red,styleCentersFaces=+] % +\end{pspicture}\end{verbatim} +\end{example} + +The color, the style and the size of the centers of the cells can be +modify using the parameters {\tt colorCentersCells}, {\tt +styleCentersCells} and {\tt sizeCentersCells}. +\begin{example} +\rm + \[\psset{unit=0.8cm,drawcenterscells=true,drawcentersfaces=false} +\begin{pspicture}(-3,-3)(3,3) +\CoxeterCoordinates[choice=33,styleCentersCells=pentagon,sizeCentersCells=0.2] % +\end{pspicture} + \begin{pspicture}(-3,-3)(3,3) +\CoxeterCoordinates[choice=33,colorCentersCells=magenta,sizeCentersCells=0.1] % +\end{pspicture} + \begin{pspicture}(-3,-3)(3,3) +\CoxeterCoordinates[choice=33,colorCentersCells=red,styleCentersCells=+] % +\end{pspicture} +\] +\begin{verbatim} +\psset{unit=0.8cm,drawcenterscells=true,drawcentersfaces=false} +\begin{pspicture}(-3,-3)(3,3) +\CoxeterCoordinates[choice=33,styleCentersCells=pentagon,sizeCentersCells=0.2] % +\end{pspicture} + \begin{pspicture}(-3,-3)(3,3) +\CoxeterCoordinates[choice=33,colorCentersCells=magenta,sizeCentersCells=0.1] % +\end{pspicture} + \begin{pspicture}(-3,-3)(3,3) +\CoxeterCoordinates[choice=33,colorCentersCells=red,styleCentersCells=+] % +\end{pspicture}\end{verbatim} +\end{example} +\section{How to modify or add a polytope to the Library} +The polytopes described in this library are the regular complex +polytopes as considered by Coxeter \cite{Cox}. But, in fact, the +same library can be used to draw any kind of polytopes (not +necessarily regular) if the user add the datas corresponding to the +vertices, the edges, the faces and the cells of the polytopes. + +To add a polytope, one has to modify the file {\tt +pst-coxeterp.pro}. This file contains the list of the polytopes +which can be drawn with the macro {\tt CoxeterCoordinates}. + For each polytope, the datas are organized as follows + \begin{verbatim} + /cox+name+datas{% The name of the Polytope + /ListePoints [ + % List of the edges + ] def + /ListeFaces [ + % List of the centers of the faces + ] def + /ListeCells [ + % List of the centers of the cells + ] def + /NbrFaces nf def % nb of faces + /NbrCells nc def % nb of cells + /NbrEdges ne def % nb of edges + /NbrVerticesInAnEdge nv def % nb of vertices per edge + } def + \end{verbatim} + The list {\tt /ListePoints} contains the description of the edges + of the polytope. The variable {\tt /NbrEdges} contains the number + of edges and the variables {\tt /NbrVerticesInAnEdges} contains the + number of vertices by edges. An edge is defined by its {\tt + /NbrVerticesInAnEdges} vertices. The list {\tt /ListePoints} of the + edges is the list of all edges described by the sequence of their + vertices. + \begin{example}\rm + Let us explain the structure on the example of the complex polytope + $3\{4\}2$. +\begin{verbatim} +/cox342datas{% + /ListePoints [ + [-1.054405725 .6087614291] + [-1.717232873 -.9914448614] + [0 -.7653668647] + [1.054405725 .6087614291] + [1.717232873 -.9914448614] + [0 -.7653668647] + [-.6628271482 .3826834323] + [0 -1.217522858] + [-1.717232873 -.9914448614] + [0 1.982889723] + [.6628271482 .3826834323] + [-1.054405725 .6087614291] + [.6628271482 .3826834323] + [0 -1.217522858] + [1.717232873 -.9914448614] + [0 1.982889723] + [-.6628271482 .3826834323] + [1.054405725 .6087614291] + ] def + /ListeFaces [ + [0 0] + ] def + /NbrFaces 1 def + /ListeCells [ + [0 0] + ] def + /NbrCells 1 def + /NbrEdges 6 def + /NbrVerticesInAnEdge 3 def + } def +\end{verbatim} + This is a complex polygon and the number $3$ indicates + that each edges is triangular and contains $3$ vertices. Hence, the + list {\tt /ListePoints} is a sequence of triplet of points. + For example, the first edge is constituted by the three vertices {\tt [-1.054405725 .6087614291] [-1.717232873 -.9914448614] + [0 -.7653668647]}. +Here, since there is $6$ edges of $3$ vertices, the list {\tt +/ListePoints} contains $18$ points with two coordinates.\\ Note +that, since $3\{4\}2$ is a polygon, it has neither faces nor cells. +In such a case, the variables {\tt ListeFaces} and {\tt ListeCells} +must contain only one point {\tt [0 0]} and the variables {\tt +/NbrFaces} and {\tt /NbrCells} contain $1$. + \end{example} +When the polytope has more than two dimensions, it has faces. The +number of faces is given by the variable {\tt /NbrFaces} and the +variable {\tt /ListeFaces} contains the list of the centers of the +faces.\\ +If the polytope has four dimensions, it has cells. The number of +cells is given by the variable {\tt /NbrCells} and the variable {\tt +/ListeCells} contains the list of the centers of the cells.\\ \\ +To add a polytope, add the datas in the files {\tt pst-coxeter.pro} +and modify the file {\tt pst-coxeter.tex} as follows. Change the +numbers of the polytopes at the line 26 of the file + \begin{verbatim} + %%% Parameter choice. Allows to choice the polytope. To each integer + %%% 0<i<81 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}} + \end{verbatim} +Here, the number of polytope is $80$, if your add other datas you +must increase this number. + \begin{verbatim} + %%% Parameter choice. Allows to choice the polytope. To each integer + %%% 0<i<82 corresponds a polytope. + \define@key[psset]{pst-coxeter}{choice}{% + \pst@cntg=#1\relax \ifnum\pst@cntg>81 \typeout{choice < or = 81 and + not `\the\pst@cntg'. Value 1 forced.} \pst@cntg=1 + \fi + \edef\psk@pstCoxeter@choice{#1}} + \end{verbatim} + Hence, you must add the polytope to the list of polytopes (line 169 +- 251 of the file {\tt pst-coxcoor.tex}. +\begin{verbatim} + /choice \the\pst@cntg\space def + choice 1 eq {cox233datas} if + ... + choice 78 eq {cox362datas} if + choice 79 eq {cox25223232datas} if + choice 80 eq {cox23232522datas} if +%%% <-- add new polytope here + \end{verbatim} + For example, add the line + \begin{verbatim} + choice 81 eq {coxNEWdatas} if + \end{verbatim} + \begin{thebibliography}{ABC} +\bibitem{qutrit} E. Briand, J.-G. Luque, J.-Y. Thibon and F. Verstrate, {\it the +moduli space of the three qutrit states},Journal of Mathematical +Physics, vol. 45, num. 12, pp. 4855--4867, 2004. +% +\bibitem{Reg} H. S. M. Coxeter, {\em Regular polytopes}, Third +Edition, Dover Publication Inc., New-York, 1973. +% +\bibitem{Cox} +H. S. M. Coxeter, {\em Regular Complex Polytopes}, Second Edition, +Cambridge University Press, 1991 . +% +\bibitem{Kalei} + H.S.M. Coxeter, {\em Kaleidoscopes, selected writing of H.S.M. + Coxeter by F.A. Sherk, P. McMullen, A.C. Thompson, A. Ivi\'c Weiss}, Canadian Mathematical Society Series of Monographs and + Advanced texts, Published in conjunction with the fiftieth anniversary of + the canadian mathematical society, J. M. Borwein and P. B. Borwein + Ed., A Wiley-Interscience publication, 1995. +% +\bibitem{Luque} J.-G. Luque, {\em Invariants des hypermatrices}, +habilitation \`a diriger les recherches, Université Paris-Est, +Décembre 2007. +% +\bibitem{Sh} G.C. Shephard, {\em Regular Complex Polytopes}, +Proceeding of the London Mathermatical Society (3), 2 82-97. +% +\bibitem{ST} G.C. Shephard and J.A. Todd, {\it Finite unitary +reflection groups}, Canadian Journal of Mathematics 6, 274-304, +1954. +% +\bibitem{Som} M.Y. Sommerville, {\it Geometry of $n$ dimension}, +Methuen, Lodon, 1929. +\end{thebibliography} + + \end{document} diff --git a/Master/texmf-dist/doc/generic/pst-cox/pst-coxeterp/Gallery.tex b/Master/texmf-dist/doc/generic/pst-cox/pst-coxeterp/Gallery.tex new file mode 100644 index 00000000000..7d47fd13eb0 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-cox/pst-coxeterp/Gallery.tex @@ -0,0 +1,342 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% pst-coxeter_parameter\Gallery.tex +% Authors: J.-G. Luque and M. Luque +% Purpose: Demonstration of the library 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/>. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\documentclass[a4paper]{article} +\usepackage[latin1]{inputenc}% +\usepackage[margin=2cm]{geometry} +\usepackage{pst-coxeterp} +\usepackage{multido} +\usepackage{amssymb} +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{graphics} +% d\'emonstration +% JG Luque 12 août 2003 +\newcount\ChoicePolytope +\def\S{\mbox{\goth S}} +\def\Sym{{\bf Sym}} +\def\sym{{\sl Sym}} +\def\QSym{{QSym}} +\def\N{{\mathbb N}}\def\L{{\mathbb L}} +\def\C{{\mathbb C}} +\def\Z{{\mathbb Z}} +\def\R{{\mathbb R}} +\def\Q{{\mathbb Q}} +\def\demoPolytopes#1{%} +\begin{center} +\ifcase\ichoice\or \def\polname{$2\{3\}3$}\def\ep{0.5mm} + \or \def\polname{$3\{3\}2$}\def\ep{0.3mm}\or +\def\polname{$3\{3\}3$}\def\ep{0.3mm}\or + \def\polname{$3\{4\}2$}\def\ep{0.3mm}\or \def\polname{$3\{4\}4$}\def\ep{0.1mm} + \or \def\polname{$3\{4\}3$}\def\ep{0.1mm}\or \def\polname{$4\{3\}4$}\def\ep{0.1mm}\or +\def\polname{$2\{4\}3\{3\}3$}\def\ep{0.1mm}\or \def\polname{ Hessien}\def\ep{0.1mm} + \or \def\polname{$3\{3\}3\{4\}2$}\def\ep{0.1mm} + \or \def\polname{de Witting} \def\ep{0.01mm} \or + \def\polname{$3\{8\}2$} \def\ep{0.1mm} \or + \def\polname{$2\{8\}3$} \def\ep{0.1mm} \or + \def\polname{$3\{5\}3$} \def\ep{0.1mm} + \or\def\polname{$4\{4\}3$} \def\ep{0.1mm} + \or\def\polname{$4\{3\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{3\}4$} \def\ep{0.1mm} + \or\def\polname{$2\{6\}4$} \def\ep{0.1mm} + \or\def\polname{$4\{6\}2$} \def\ep{0.1mm} + \or\def\polname{$5\{3\}5$} \def\ep{0.1mm} + \or\def\polname{$2\{10\}3$} \def\ep{0.1mm} + \or\def\polname{$3\{10\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{5\}3$} \def\ep{0.1mm} + \or\def\polname{$3\{5\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{4\}3$} \def\ep{0.1mm} + \or\def\polname{$2\{3\}2\{4\}3$} \def\ep{0.1mm} + \or\def\polname{$3\{4\}2\{3\}2$} \def\ep{0.1mm} + \or\def\polname{$3\{4\}2\{3\}2\{3\}2$} \def\ep{0.1mm} + \or\def\polname{$2\{3\}2\{3\}2\{4\}3$} \def\ep{0.1mm} + \fi {\Huge Polytope \polname} + +\begin{pspicture}(-9,-9)(9,9) +\psset{unit=3cm,linewidth=0.01mm} +\CoxeterCoordinates[choice=#1,linewidth=\ep] % par défaut choice=1 (332) +\end{pspicture} + +$\backslash$\texttt{CoxeterCoordinates[choice=#1]} +\end{center} +\begin{center} +\begin{tabular}{ccc} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawvertices=false,choice=#1,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawcenters=false,choice=#1,linewidth=0.01mm] % +\end{pspicture} +& +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.7cm} +\CoxeterCoordinates[drawedges=false,choice=#1,linewidth=0.01mm] % +\end{pspicture}\\ +\texttt{[drawvertices=false,choice=#1]} +& +\texttt{[drawcenters=false,choice=#1]} +& +\texttt{[drawedges=false,choice=#1]} +\end{tabular} +\end{center}} +% +\title{The Gallery of Infinite Series} +\author{Jean-Gabriel \textsc{Luque}\footnote{Jean-Gabriel.Luque@univ-mlv.fr}, +Manuel \textsc{Luque}\footnote{manuel.luque27@gmail.com}} +\begin{document} +\maketitle +\newpage +\section{Real polygons} +There are the polytopes $2\{\frac pq\}2$ (with $p$ and $q$ in $\N$) +in the notation of Coxeter. Use the command: +\begin{verbatim} +\psset{unit=1.5cm}\Polygon[P=p,Q=q] +\end{verbatim} +\[\begin{array}{|c|c|c|} +\hline 2&3&4\\ +\hline \begin{pspicture}(-1.5,-3)(1.5,3) +\psset{unit=1.5cm}\Polygon[P=2,Q=1] +\end{pspicture}&\begin{pspicture}(-3,-3)(3,3) +\psset{unit=1.5cm}\Polygon[P=3] +\end{pspicture}&\begin{pspicture}(-3,-3)(3,3) +\psset{unit=1.5cm}\Polygon[P=4] +\end{pspicture}\\ +\hline 5&\frac52&6\\ +\hline \begin{pspicture}(-1.5,-3)(1.5,3) +\psset{unit=1.5cm}\Polygon[P=5,Q=1] +\end{pspicture}&\begin{pspicture}(-3,-3)(3,3) +\psset{unit=1.5cm}\Polygon[P=5,Q=2] +\end{pspicture}&\begin{pspicture}(-3,-3)(3,3) +\psset{unit=1.5cm}\Polygon[P=6] +\end{pspicture}\\ +\hline 7&\frac72&\frac73\\ +\hline \begin{pspicture}(-1.5,-3)(1.5,3) +\psset{unit=1.5cm}\Polygon[P=7] +\end{pspicture}&\begin{pspicture}(-3,-3)(3,3) +\psset{unit=1.5cm}\Polygon[P=7,Q=2] +\end{pspicture}&\begin{pspicture}(-3,-3)(3,3) +\psset{unit=1.5cm}\Polygon[P=10,Q=3] +\end{pspicture}\\ +\hline +\end{array} +\] +\newpage +\section{Simplices } +There are the real polytopes $2\{3\}2\cdots2\{3\}2$ in dimension $n$ +(tetrahedron, pentatope, sextatope etc...) in the notation of +Coxeter. Use the command: +\begin{verbatim} +\psset{unit=1.5cm}\Simplex[dimension=n] +\end{verbatim} +\[\begin{array}{|c|c|c|} +\hline 2&3&4\\ +\hline \begin{pspicture}(-1.5,-3)(1.5,3) +\psset{unit=1.5cm}\Simplex[dimension=2] +\end{pspicture}&\begin{pspicture}(-3,-3)(3,3) +\psset{unit=1.5cm}\Simplex[dimension=3] +\end{pspicture}&\begin{pspicture}(-3,-3)(3,3) +\psset{unit=1.5cm}\Simplex[dimension=4] +\end{pspicture}\\ +\hline 5&6&7\\ +\hline \begin{pspicture}(-1.5,-3)(1.5,3) +\psset{unit=1.5cm}\Simplex[dimension=5] +\end{pspicture}&\begin{pspicture}(-3,-3)(3,3) +\psset{unit=1.5cm}\Simplex[dimension=6] +\end{pspicture}&\begin{pspicture}(-3,-3)(3,3) +\psset{unit=1.5cm}\Simplex[dimension=7] +\end{pspicture}\\ +\hline 8&9&10\\ +\hline \begin{pspicture}(-1.5,-3)(1.5,3) +\psset{unit=1.5cm}\Simplex[dimension=8] +\end{pspicture}&\begin{pspicture}(-3,-3)(3,3) +\psset{unit=1.5cm}\Simplex[dimension=9] +\end{pspicture}&\begin{pspicture}(-3,-3)(3,3) +\psset{unit=1.5cm}\Simplex[dimension=10] +\end{pspicture}\\ +\hline +\end{array} +\]\newpage +\section{The infinite series $\gamma_n^p$} +It is an infinite series of polytopes with two parameters $p$ and +$n$. The parameter $n$ is the dimension of the polytope. In the +notation of Coxeter, its name reads $p\{4\}2\{3\}\dots\{3\}2$. In +the case $p=2$, we recovers the family of the hypercubes. Use the +command: + \begin{verbatim} + \gammapn[P=p,dimension=n] + \end{verbatim} +\[\begin{array}{|c|c|c|} +\hline \gamma_2^2&\gamma_2^3&\gamma_2^4\\ +\hline \begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.2cm}\gammapn[dimension=2,P=2,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.2cm}\gammapn[P=3,dimension=2,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1cm}\gammapn[P=4,dimension=2,linewidth=0.01mm] +\end{pspicture}\\ +\hline \gamma_3^2&\gamma_3^3&\gamma_3^4\\ \hline +\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1cm}\gammapn[P=2,dimension=3,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=0.8cm}\gammapn[P=3,dimension=3,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=0.7cm}\gammapn[P=4,dimension=3,linewidth=0.01mm] +\end{pspicture}\\ +\hline \gamma_4^2&\gamma_4^3&\gamma_4^4\\ +\hline \begin{pspicture}(-2,-3)(2,3) +\psset{unit=0.8cm}\gammapn[P=2,dimension=4,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=0.6cm}\gammapn[P=3,dimension=4,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=0.55cm}\gammapn[P=4,dimension=4,linewidth=0.01mm] +\end{pspicture}\\ +\hline +\end{array} +\]% +\newpage +\section{The infinite series $\beta_n^p$} +It is an infinite series of polytopes with two parameters $p$ and +$n$ reciprocals of $\gamma_n^p$. The parameter $n$ is the dimension +of the polytope. In the notation of Coxeter, its name reads +$2\{3\}2\{3\}\dots\{3\}2\{4\}p$. In the case $p=2$, we recovers the +family of the $2^n$-topes which generalizes the tetrahedron for +higher dimension. Use the command: + \begin{verbatim} + \betapn[P=p,dimension=n] + \end{verbatim} +\[\begin{array}{|c|c|c|} +\hline \beta_2^2&\beta_2^3&\beta_2^4\\ +\hline \begin{pspicture}(-2,-3)(2,3) +\psset{unit=2cm}\betapn[dimension=2,P=2] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.5cm}\betapn[P=3,dimension=2,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.4cm}\betapn[P=4,dimension=2,linewidth=0.01mm] +\end{pspicture}\\ +\hline \beta_3^2&\beta_3^3&\beta_3^4\\ \hline +\begin{pspicture}(-2,-3)(2,3) +\psset{unit=2cm}\betapn[P=2,dimension=3,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.5cm}\betapn[P=3,dimension=3,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.4cm}\betapn[P=4,dimension=3,linewidth=0.01mm] +\end{pspicture}\\ +\hline \beta_4^2&\beta_4^3&\beta_4^4\\ +\hline \begin{pspicture}(-2,-3)(2,3) +\psset{unit=2cm}\betapn[P=2,dimension=4,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.5cm}\betapn[P=3,dimension=4,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.4cm}\betapn[P=4,dimension=4,linewidth=0.01mm] +\end{pspicture}\\ +\hline +\end{array} +\]% +\newpage +\section{The infinite series $\gamma_2^p$} +It is a special case of the series $\gamma_n^p$ for $n=2$. In this +case, the polytopes are complex polygons. The projection used here +is different than the projection used with {\tt gammapn}. Use the +command: +\begin{verbatim} +\gammaptwo[P=p] +\end{verbatim} +\[\begin{array}{|c|c|c|} +\hline \gamma_2^3&\gamma_2^4&\gamma_2^5\\ +\hline \begin{pspicture}(-2,-3)(2,3) \psset{unit=1cm}\gammaptwo[P=3] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1cm}\gammaptwo[P=4,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1cm}\gammaptwo[P=5,linewidth=0.01mm] +\end{pspicture}\\ +\hline \gamma_2^6&\gamma_2^7&\gamma_2^8\\ \hline +\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1cm}\gammaptwo[P=6,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=0.8cm}\gammaptwo[P=7,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=0.7cm}\gammaptwo[P=8,linewidth=0.01mm] +\end{pspicture}\\ +\hline \gamma_2^9&\gamma_2^{10}&\gamma_2^{11}\\ +\hline \begin{pspicture}(-2,-3)(2,3) +\psset{unit=0.8cm}\gammaptwo[P=9,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=0.7cm}\gammaptwo[P=10,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=0.7cm}\gammaptwo[P=11,linewidth=0.01mm] +\end{pspicture}\\ +\hline +\end{array} +\]% +\newpage +\section{The infinite series $\beta_2^p$} +It is a special case of the series $\beta_n^p$ for $n=2$. In this +case, the polytopes are complex polygons. The projection used here +is different than the projection used with {\tt betapn}. Use the +command: +\begin{verbatim} +\betaptwo[P=p] +\end{verbatim} +\[\begin{array}{|c|c|c|} +\hline \beta_2^3&\beta_2^4&\beta_2^5\\ +\hline \begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.5cm}\betaptwo[P=3] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.5cm}\betaptwo[P=4,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.5cm}\betaptwo[P=5,linewidth=0.01mm] +\end{pspicture}\\ +\hline \beta_2^6&\beta_2^7&\beta_2^8\\ \hline +\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.5cm}\betaptwo[P=6,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.5cm}\betaptwo[P=7,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.5cm}\betaptwo[P=8,linewidth=0.01mm] +\end{pspicture}\\ +\hline \beta_2^9&\beta_2^{10}&\beta_2^{11}\\ +\hline \begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.5cm}\betaptwo[P=9,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.5cm}\betaptwo[P=10,linewidth=0.01mm] +\end{pspicture}&\begin{pspicture}(-2,-3)(2,3) +\psset{unit=1.5cm}\betaptwo[P=11,linewidth=0.01mm] +\end{pspicture}\\ +\hline +\end{array} +\]% +\begin{thebibliography}{ABC} +% +\bibitem{Cox1} +H. S. M. Coxeter, {\em Regular Complex Polytopes}, Second Edition, +Cambridge University Press, 1991 . +% +\end{thebibliography} +\end{document} diff --git a/Master/texmf-dist/doc/generic/pst-cox/pst-coxeterp/pst-coxeterp_doc.pdf b/Master/texmf-dist/doc/generic/pst-cox/pst-coxeterp/pst-coxeterp_doc.pdf Binary files differnew file mode 100644 index 00000000000..efc7bfa09f5 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-cox/pst-coxeterp/pst-coxeterp_doc.pdf diff --git a/Master/texmf-dist/doc/generic/pst-cox/pst-coxeterp/pst-coxeterp_doc.tex b/Master/texmf-dist/doc/generic/pst-cox/pst-coxeterp/pst-coxeterp_doc.tex new file mode 100644 index 00000000000..4cb0c32a187 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-cox/pst-coxeterp/pst-coxeterp_doc.tex @@ -0,0 +1,470 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% pst-coxeter_parameter\pst-coxeterp_doc.tex +% Authors: J.-G. Luque and M. Luque +% Purpose: Documentation for the library pst-coxcoor +% 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/>. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\documentclass[a4paper]{article} +\usepackage[latin1]{inputenc}% +\usepackage[margin=2cm]{geometry} +\usepackage{pst-coxeterp} +\usepackage{multido} +\usepackage{amssymb} +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{graphics} +% d\'emonstration +% JG Luque 12 août 2003 +\newtheorem{example}{Example}[section] +\newcount\ChoicePolytope +\def\C{{\mathbb C}} + +\title{The Library {\tt pst-coxeterp}} +\author{Jean-Gabriel \textsc{Luque}\footnote{Universit\'e Paris-Est, Laboratoire d'informatique +de l'Institut-Gaspard Monge, Jean-Gabriel.Luque@univ-mlv.fr} and +Manuel + \textsc{Luque}\footnote{mluque5130@aol.com}} +\begin{document} +\maketitle + \begin{abstract} + We describe the {\tt LaTex} library {\tt pst-coxeterp} devoted to + draw regular complex polytopes belonging in the infinite series. + \end{abstract} + \section{Introduction} + Inspired by the dissertation of G.C. Shephard \cite{Sh}, Coxeter + toke twenty years to write his most famous book {\em Regular Complex Polytopes} \cite{Cox}. But its + interest for the polytope dates from the beginning of his career as + shown his numerous publications on the subject (reader can refer to + \cite{Reg} or \cite{Kalei}). According to the preface of + \cite{Cox}, the term of complex polytopes is due to D.M.Y. + Sommerville \cite{Som}. A complex polytope may have more than two + vertices on an edge (and in particular the polygons may have more + than two edges at a vertice). It is a finite set of flags of subspaces in $\C^n$ + with certain constraints + which will be not explain here \footnote{For a precise + definition, see \cite{Cox} Ch12}. + In fact, a complex polytope can be generated from one vertice by a finite number of pseudo-reflections. + More precisely, as for the classical solids, it + can be constructed from an arrangement of mirrors, + considering a point in the intersection of all but one the mirrors + and computing the orbit of this point by the pseudo-reflections generated by the mirrors. In the + case of the real polytopes, one uses classical reflections which are + involutions. It is not the case for general complex polytopes, since + a reflection may include a component which is a rotation. +The classification of the complex polytopes is due to G.C. Shephard +\cite{Sh} and is closely related to the classification of the +complex unitary reflection groups \cite{ST}. This classification +includes four infinite series of polytopes: the well-known real +polygons (including the starry polygon) which have two parameters, +the series of simplices (triangle, tetrahedron, pentatope, sextatope +etc...) which have only one parameter, the dimension and to +reciprocal series $\gamma_n^p$ and $\beta_n^p$. The library +described here is a {\tt LaTex} package for drawing the polytopes of +these infinite series. +\section{Install {\tt pst-coxeterp}} +The package contains two files: A latex style file {\tt +pst-coxeterp.sty} which call the latex file {\tt pst-coxeterp.tex} +containing the description of the macros. The installation is very +simple. It suffices to copy the files {\tt pst-coxeterp.sty} and +{\tt pst-coxeterp.tex} in the appropriate directories. +\begin{example}\rm +The file {\tt pst-coxeterp.sty} may be copy in the directory \\ {\tt +c:/texmf/tex/latex/pst-coxeterp},\\ + the file {\tt pst-coxeterp.tex} in\\ +{\tt c:/texmf/tex/generic/pst-coxeterp} +\end{example} +To use the package add the code +\begin{verbatim} +\usepackage{pst-coxeterp} +%\end{verbatim} +in the beginning of your LaTex-file. +\begin{example}\rm +\begin{verbatim} +\documentclass[a4paper]{article} +... +\usepackage{pst-coxeterp} +.... +\end{verbatim} +\end{example} +The library needs the packages {\tt PSTrick} and {\tt pst-xkey}.% + +\section{The different families} +This library contains six macros for drawing polytopes belonging in +a infinite series.\\ +The first macro, {\tt Polygon}, draws real (starry or not) polygon. +The polygon is defined by two parameters {\tt P} and {\tt Q} which +defines the angle $2\frac QP\Pi $ between the segment from the +center to the first vertices and the segment from the center to the +second vertices. By default the value of {\tt Q} is $1$. +\begin{example} +\begin{pspicture}(-2,-2)(2,2) +\Polygon[P=11,Q=1] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\Polygon[P=11,Q=3] +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) + \Polygon[P=11,Q=4] +\end{pspicture} +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\Polygon[P=11,Q=1] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\Polygon[P=11,Q=3] +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) + \Polygon[P=11,Q=4] +\end{pspicture} +\end{verbatim} +\end{example} + +The macro {\tt Simplex} draws simplices in dimension $n$. The +simplices are the real polytopes whose automorphism groups are the +symmetric groups. The dimension of the polytope can be chosen using +the parameter {\tt dimension}. +\begin{example} +\begin{pspicture}(-2,-2)(2,2) +\Simplex[dimension=2] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\Simplex[dimension=3] +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) + \Simplex[dimension=5] +\end{pspicture} +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\Simplex[dimension=2] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\Simplex[dimension=3] +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) + \Simplex[dimension=5] +\end{pspicture} +\end{verbatim} +\end{example} + +The polytopes $\gamma_n^p$ forms a two parameters family which +contains as special case the hypercubes. The parameter $n$ is the +dimension of the polytope and the parameter $p$ is the number of +vertices per edge. Use the macro {\tt gammapn} and the parameters +{\tt dimension} and {\tt P} to chose the characteristics of the +polytope. +\begin{example} +\begin{pspicture}(-2,-2)(2,2) +\gammapn[dimension=2,P=4] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\gammapn[dimension=3,P=3,unit=0.7cm] +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) + \gammapn[dimension=5,P=2,unit=0.55cm] +\end{pspicture} +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\gammapn[dimension=2,P=4] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\gammapn[dimension=3,P=3,unit=0.7cm] +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) + \gammapn[dimension=5,P=2,unit=0.55cm] +\end{pspicture} +\end{verbatim} +\end{example} + +The polytopes $\beta_n^p$ forms a two parameters family which +contains as special case the hyperoctahedra. The parameter $n$ is +the dimension of the polytope and the parameter $p$ is the number of +cells of dimension $n-1$ containing a cell of dimension $n-2$. Use +the macro {\tt betapn} and the parameters {\tt dimension} and {\tt +P} to chose the characteristics of the polytope. +\begin{example} +\begin{pspicture}(-2,-2)(2,2) +\betapn[dimension=2,P=4] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\betapn[dimension=3,P=3] +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) + \betapn[dimension=5,P=2] +\end{pspicture} +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\betapn[dimension=2,P=4] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\betapn[dimension=3,P=3] +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) + \betapn[dimension=5,P=2] +\end{pspicture} +\end{verbatim} +\end{example} + +The macro {\tt gammaptwo} draw the regular complex polytope +$\gamma_2^p$ which is a special case of $\gamma_n^p$ for an other +projection. Use the parameter {\tt P} for setting the number of +vertices by edge. +\begin{example} +\begin{pspicture}(-2,-2)(2,2) +\gammaptwo[P=3] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\gammaptwo[P=4] +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) + \gammaptwo[P=5] +\end{pspicture} +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\gammaptwo[P=3] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\gammaptwo[P=4] +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) + \gammaptwo[P=5] +\end{pspicture} +\end{verbatim} +\end{example} + +The macro {\tt betaptwo} draw the regular complex polytope +$\beta_2^p$ which is a special case of $\beta_n^p$ for an other +projection (the same than for {\tt gammaptwo}). Use the parameter +{\tt P} for setting the number of vertices by edge. +\begin{example} +\begin{pspicture}(-2,-2)(2,2) +\betaptwo[P=3] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\betaptwo[P=4] +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) + \betaptwo[P=5] +\end{pspicture} +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\betaptwo[P=3] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\betaptwo[P=4] +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) + \betaptwo[P=5] +\end{pspicture} +\end{verbatim} +\end{example} + +\section{Graphical parameters} +\subsection{The components of a polytope} + The library {\tt pst-coxeterrep.sty} contains macros for +drawing the vertices, the edges and the centers of the edges of +polytopes of the infinite series of regular complex polytopes. + +It is possible to choice which components of the polytope will be +drawn. It suffices to use the boolean parameters {\tt drawedges}, +{\tt drawvertices} and {\tt drawcenters}. + + By default the values of the parameters {\tt +drawedges}, {\tt drawvertices}, {\tt drawcenters} are set to {\tt +true}. +\begin{example} +\rm +\[ +\begin{pspicture}(-2,-2)(2,2) +\Polygon[P=5,Q=2,drawcenters=false] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\Simplex[dimension=3,drawvertices=false] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5} + \gammapn[P=4,dimension=4,drawedges=false] +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\Polygon[P=5,Q=2,drawcenters=false] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\Simplex[dimension=3,drawvertices=false] % +\end{pspicture} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5} + \gammapn[P=4,dimension=4,drawedges=false] +\end{pspicture}\end{verbatim} +\end{example} +\section{Graphical properties} +It is possible to change the graphical characteristics of a +polytope.\\ +The size of the polytope depends on the parameter {\tt unit}. +\begin{example} +\rm + \[ + \begin{pspicture}(-1,-1)(1,1) +\gammaptwo[P=4,unit=0.5cm] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\gammaptwo[P=4,unit=1cm] % +\end{pspicture} + \begin{pspicture}(-4,-4)(4,4) +\gammaptwo[P=4,unit=2cm] % +\end{pspicture} +\] +\begin{verbatim} + \begin{pspicture}(-1,-1)(1,1) +\gammaptwo[P=4,unit=0.5cm] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\gammaptwo[P=4,unit=1cm] % +\end{pspicture} + \begin{pspicture}(-4,-4)(4,4) +\gammaptwo[P=4,unit=2cm] % +\end{pspicture} +\end{verbatim} +\end{example} +Classically, one can modify the color and the width of the edges +using the parameter {\tt linecolor} and {\tt linewidth}. +\begin{example} +\rm + \[ +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.8,linewidth=0.01,linecolor=red} +\betaptwo[P=5] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\betaptwo[P=5] % +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.8,linewidth=0.01,linecolor=red} +\betaptwo[P=5] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\betaptwo[P=5] % +\end{pspicture} +\end{verbatim} +\end{example} +The color, the style and the size of the vertices can be modify +using the parameters {\tt colorVertices}, {\tt styleVertices} and +{\tt sizeVertices}. The style of the vertices can be chosen in the +classical dot styles. +\begin{example} +\rm + \[ +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.5cm,colorVertices=blue,styleVertices=pentagon,sizeVertices=0.2} +\betapn[P=5,dimension=4] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.5cm,colorVertices=magenta,sizeVertices=0.1,styleVertices=triangle} % +\betapn[P=5,dimension=4] +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.5cm,colorVertices=red,styleVertices=+,sizeVertices=0.2} % +\betapn[P=5,dimension=4] +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.5cm,colorVertices=blue,styleVertices=pentagon,sizeVertices=0.2} +\betapn[P=5,dimension=4] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.5cm,colorVertices=magenta,sizeVertices=0.1,styleVertices=triangle} % +\betapn[P=5,dimension=4] +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=1.5cm,colorVertices=red,styleVertices=+,sizeVertices=0.2} % +\betapn[P=5,dimension=4] +\end{pspicture} +\end{verbatim} +\end{example} +The color, the style and the size of the centers of the edges can be +modify using the parameters {\tt colorCenters}, {\tt styleCenters} +and {\tt sizeCenters}. +\begin{example} +\rm + \[ +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm,colorCenters=blue,styleCenters=pentagon,sizeCenters=0.2} % +\gammapn[P=5,dimension=4] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm,colorCenters=magenta,sizeCenters=0.1,styleCenters=triangle} % +\gammapn[P=5,dimension=4] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm,colorCenters=red,styleCenters=+,sizeCenters=0.2} % +\gammapn[P=5,dimension=4] % +\end{pspicture} +\] +\begin{verbatim} +\begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm,colorCenters=blue,styleCenters=pentagon,sizeCenters=0.2} % +\gammapn[P=5,dimension=4] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm,colorCenters=magenta,sizeCenters=0.1,styleCenters=triangle} % +\gammapn[P=5,dimension=4] % +\end{pspicture} + \begin{pspicture}(-2,-2)(2,2) +\psset{unit=0.5cm,colorCenters=red,styleCenters=+,sizeCenters=0.2} % +\gammapn[P=5,dimension=4] % +\end{pspicture} +\end{verbatim} +\end{example} + + \begin{thebibliography}{ABC} + +\bibitem{Reg} H. S. M. Coxeter, {\em Regular polytopes}, Third +Edition, Dover Publication Inc., New-York, 1973. +% +\bibitem{Cox} +H. S. M. Coxeter, {\em Regular Complex Polytopes}, Second Edition, +Cambridge University Press, 1991 . +% +\bibitem{Kalei} + H.S.M. Coxeter, {\em Kaleidoscopes, selected writing of H.S.M. + Coxeter by F.A. Sherk, P. McMullen, A.C. Thompson, A. Ivi\'c Weiss}, Canadian Mathematical Society Series of Monographs and + Advanced texts, Published in conjunction with the fiftieth anniversary of + the canadian mathematical society, J. M. Borwein and P. B. Borwein + Ed., A Wiley-Interscience publication, 1995. +% +\bibitem{Sh} G.C. Shephard, {\em Regular Complex Polytopes}, +Proceeding of the London Mathermatical Society (3), 2 82-97. +% +\bibitem{ST} G.C. Shephard and J.A. Todd, {\it Finite unitary +reflection groups}, Canadian Journal of Mathematics 6, 274-304, +1954. +% +\bibitem{Som} M.Y. Sommerville, {\it Geometry of $n$ dimension}, +Methuen, Lodon, 1929. +\end{thebibliography} + + \end{document} diff --git a/Master/texmf-dist/dvips/pst-cox/pst-coxeter.pro b/Master/texmf-dist/dvips/pst-cox/pst-coxeter.pro new file mode 100644 index 00000000000..324f86bc3e0 --- /dev/null +++ b/Master/texmf-dist/dvips/pst-cox/pst-coxeter.pro @@ -0,0 +1,83406 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% polygonesCoordinate\pst-coxeter.pro +% Authors: J.-G. Luque and M. Luque +% Purpose: Datas for the library pst-coxcoor +% 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/>. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/cox233datas{%nbaretes := 24; +%nbsommetspararetes := 2; +/ListePoints [ + [0.00600 0.0100] + [-1.94 -0.00600] + [1.67 -0.965] + [-0.965 1.68] + [0.0100 -0.00600] + [-0.00600 1.94] + [0.00600 -1.94] + [-0.0100 0.00600] + [0.965 1.67] + [0.00600 0.0100] + [0.965 1.67] + [-1.68 -0.965] + [-1.68 -0.965] + [1.94 0.00600] + [1.67 -0.965] + [0.0100 -0.00600] + [1.94 0.00600] + [-0.00600 -0.0100] + [-0.00600 -0.0100] + [-0.965 -1.67] + [-1.67 0.965] + [0.965 -1.68] + [0.00600 -1.94] + [-0.965 1.68] + [-1.67 0.965] + [-0.0100 0.00600] + [1.68 0.965] + [-0.965 -1.67] + [0.965 -1.68] + [-0.00600 1.94] + [-1.68 -0.965] + [0.0100 -0.00600] + [1.67 -0.965] + [-1.94 -0.00600] + [-0.00600 1.94] + [-0.965 -1.67] + [0.00600 0.0100] + [0.965 -1.68] + [-1.67 0.965] + [1.94 0.00600] + [0.965 1.67] + [0.00600 -1.94] + [-1.94 -0.00600] + [1.68 0.965] + [-0.965 1.68] + [-0.00600 -0.0100] + [-0.0100 0.00600] + [1.68 0.965] +] def +/ListeFaces [[0 0]] def +/NbrFaces 1 def +/ListeCells [[0 0]] def +/NbrCells 1 def +/NbrEdges 24 def +/NbrVerticesInAnEdge 2 def +} def +% +/cox332datas{% +%nbaretes := 16 +%nbsommetspararetes := 3 +/ListePoints [ +[-.766 1.32] +[-.757 -.203] +[.557 .566] +[.300e-2 1.53] +[-1.32 -.766] +[1.33 -.766] +[.566 -.557] +[-.766 .212] +[-.766 -1.33] +[-.203 .757] +[-1.53 .300e-2] +[-.212 -.766] +[.566 -.557] +[1.32 .766] +[-.203 .757] +[-1.33 .766] +[-.557 -.566] +[.212 .766] +[1.32 .766] +[-1.33 .766] +[-.300e-2 -1.53] +[.757 .203] +[-.557 -.566] +[.766 -1.32] +[-1.53 .300e-2] +[.766 -1.32] +[.766 1.33] +[-.766 .212] +[.757 .203] +[.300e-2 1.53] +[-1.32 -.766] +[.203 -.757] +[-.566 .557] +[-.212 -.766] +[1.33 -.766] +[.557 .566] +[-.300e-2 -1.53] +[.766 -.212] +[-.757 -.203] +[1.53 -.300e-2] +[.212 .766] +[.203 -.757] +[.766 -.212] +[.766 1.33] +[-.566 .557] +[-.766 -1.33] +[1.53 -.300e-2] +[-.766 1.32] +]def +/ListeFaces [[0 0]] def +/NbrFaces 1 def +/ListeCells [[0 0]] def +/NbrCells 1 def +/NbrEdges 16 def +/NbrVerticesInAnEdge 3 def} def +% +/cox333datas{% +%nbaretes := 8 +%nbsommetspararetes := 3 +/ListePoints [ + [-1. -.5323836407] + [0 -2.264434449] + [1. -.5323836407] + [-1.922115513 0] + [1. -.5323836407] + [0 2.264434449] + [-1.922115513 0] + [0 -2.264434449] + [1. .5323836407] + [-1.922115513 0] + [-1. -.5323836407] + [-1. .5323836407] + [-1. -.5323836407] + [1.922115513 0] + [0 2.264434449] + [-1. .5323836407] + [0 -2.264434449] + [1.922115513 0] + [-1. .5323836407] + [1. .5323836407] + [0 2.264434449] + [1. .5323836407] + [1. -.5323836407] + [1.922115513 0] + ]def + /ListeFaces [[0 0]] def +/NbrFaces 1 def +/ListeCells [[0 0]] def +/NbrCells 1 def +/NbrEdges 8 def +/NbrVerticesInAnEdge 3 def +} def +% +/cox342datas{% +/ListePoints [[-1.054405725 .6087614291] + [-1.717232873 -.9914448614] + [0 -.7653668647] + [1.054405725 .6087614291] + [1.717232873 -.9914448614] + [0 -.7653668647] + [-.6628271482 .3826834323] + [0 -1.217522858] + [-1.717232873 -.9914448614] + [0 1.982889723] + [.6628271482 .3826834323] + [-1.054405725 .6087614291] + [.6628271482 .3826834323] + [0 -1.217522858] + [1.717232873 -.9914448614] + [0 1.982889723] + [-.6628271482 .3826834323] + [1.054405725 .6087614291]] def +/ListeFaces [[0 0]] def +/NbrFaces 1 def +/ListeCells [[0 0]] def +/NbrCells 1 def +/NbrEdges 6 def +/NbrVerticesInAnEdge 3 def +} def +% +/cox344datas{% +%nbaretes := 96 +%nbsommetspararetes := 3 +/ListePoints [ + [1.012198956 -.5794688850] + [2.814462272 -.6446362499] + [1.969767208 .9487532482] + [-2.115077701 1.965502504] + [-1.428428653 1.747514995] + [-1.582970456 2.451164269] + [-.9444885464 .8034427549] + [1.012198956 -.5794688850] + [1.231491816 1.806528019] + [-1.428428653 1.747514995] + [.2235575635 1.219672452] + [-.1453104939 2.914255753] + [-.5868555670 1.007934253] + [.7991780521 2.110812998] + [-.8489597677 2.759713951] + [-1.166324453 -.42647027e-2] + [-2.759713951 -.8489597671] + [-1.231491816 -1.806528019] + [-.5868555670 1.007934253] + [.9444885464 -.8034427549] + [1.747514995 1.428428653] + [-.2235575635 -1.219672452] + [-1.969767208 -.9487532482] + [-1.331285297 -2.596474762] + [-2.451164269 -1.582970455] + [-.7991780521 -2.110812998] + [-1.168046109 -.4162296966] + [1.168046109 .4162296966] + [-1.007934253 -.5868555667] + [.9487532487 -1.969767208] + [-2.180245065 .1632391885] + [-.5868555670 1.007934253] + [-2.115077701 1.965502504] + [-.8034427546 -.9444885460] + [-1.331285297 -2.596474762] + [.3632980041 -2.227606705] + [-2.914255752 -.1453104933] + [-2.759713951 -.8489597671] + [-2.227606705 -.3632980036] + [-2.227606705 -.3632980036] + [-1.965502504 -2.115077701] + [-.5794688848 -1.012198956] + [-2.227606705 -.3632980036] + [.426470311e-2 -1.166324452] + [-.4162296966 1.168046109] + [-1.219672452 .2235575636] + [-.7991780521 -2.110812998] + [1.012198956 -.5794688850] + [-2.451164269 -1.582970455] + [-1.965502504 -2.115077701] + [-1.747514995 -1.428428653] + 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[-1.266044443 -.7309511003 ] +[-.4999999999 -1.373738710 ] + [-.3263518228 .3889309568 ] + [-.3263518226 -.3889309570 ] + [-.1e-9 .5077133062 ] + [.6736481775 -.3889309570 ] + [.7660444431 .6427876097 ] + [0 1.461902201 ] + [-.9396926207 -1.119882057 ] + [.9396926207 1.119882057 ] + [.5000000000 -.5958767964 ] + [1.439692621 -.2538566531 ] + [-.2660444432 -.7309511003 ] + [.1736481773 .9848077531 ] + [-.9396926206 .3420201436 ] + [.5000000000 .8660254040 ] + [-1. 0 ] + [-.7660444434 .6427876099 ] + [.4396926206 -.2538566531 ] + [1. 0 ] + ] def + /ListeCells [[0 0]] def +/NbrCells 1 def +/NbrEdges 216 def +/NbrVerticesInAnEdge 2 def +/NbrFaces 72 def +}def +% +/cox33333datas{% +%nbaretes := 72 +%nbsommetspararetes := 3 +/ListePoints [ + [1.113340798 .6427876095] + [.2339555570 .6427876099] + [.6736481774 -.1187823494] + [-1.939692621 .3420201436] + [-1.113340798 .6427876101] +[-1.266044443 -.2232377941] + [0 -.6840402869] + [-1.266044443 1.508813014] +[1.266044443 1.508813014] + 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-1.285575219] + [-.5923962658 .3420201434] + [-1.705737064 -.9848077527] + [-1.939692621 .3420201436] + [-.4396926206 1.208045548] +[-.4396926206 -.5240052605] + [-.1e-9 1.969615507] + [.5923962659 .3420201435] + [-1.113340798 .6427876101] + [-.5923962658 .3420201434] + [-1.266044443 -.2232377941] + [-.4396926206 -.5240052605] + [.5923962659 .3420201435] + [1.266044443 -.2232377943] + [.4396926206 -.5240052607] + [-1.939692621 .3420201436] + [-.1e-9 1.969615507] + [.4396926206 -.5240052607] + [.2e-9 -1.285575219] + [.4396926206 -.5240052607] + [-.4396926206 -.5240052605] + [-1.939692621 .3420201436] + [-.6736481773 -1.850833157] + [.5923962659 .3420201435] + [-.6736481773 -1.850833157] + [-1.705737064 -.9848077527] + [-.4396926206 -.5240052605] + [1.266044443 -.2232377943] + [.6736481774 -1.850833158] + [-.4396926206 -.5240052605] +] def +/ListeFaces [[.3368240887 .593911746e-1 ] + [.2198463103 -.6040227739 ] + [.3368240887 .9254165786 ] + [-.9698463103 -.1710100717 ] + [-.5566703990 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+[1.4845 .10153] +[1.2748 -.40998] +[.86892 1.9134] +[-1.1938 -1.2121] +[-.72361 .92148] +[.40344 -1.1000] +[-.36216 -1.4432] +[-1.7864 .61958] +[-.12704 1.6966] +[.78518e-1 .65278] +[1.6783 .27889] +[1.9317 -1.2748] +[1.1270 2.0215] +[1.1270 -2.0215] +[-.12704 -1.6966] +[.69405 1.0255] +] def +/NbrFaces 720 def +/ListeCells [[-.16246 .35065] +[-.37917 -.92533] +[-.18819 -.33754] +[-.97148 .76287] +[1.3507 .16246] +[-.97148 -.23713] +[.99721 .92533] +[.66246 .18819] +[.57188 -1.2343] +[.52573 -.85065] +[-.66246 -.18819] +[.76287 .97148] +[-.38369 .57188] +[.35065 .16246] +[-.54163 .42533] +[-.57188 1.2343] +[.92533 -.99721] +[-.74675e-1 -.99721] +[1.1882 .33754] +[.92533 -.37917] +[.37917 .92533] +[-.64656 .23713] +[-1.0257 -.68819] +[.28329 .26287] +[-.76287 .64656] +[.23713 .64656] +[.25731e-1 .68819] +[-.28329 -.26287] +[-.66246 -1.1882] +[.68819 -.25731e-1] +[.99721 -.74675e-1] +[-1.3347 .26287] +[.74675e-1 .99721] +[-.76287 -.97148] +[-.99721 -.92533] +[-.57188 -.38369] +[1.3347 -.26287] +[.74675e-1 .37917] +[.54163 -.42533] +[.37917 -.74675e-1] +[.46151e-1 -.38369] +[.57188 .38369] +[-.68819 1.0257] +[.76287 -.64656] +[-.33754 .18819] +[-.64656 -.76287] +[.33754 -.18819] +[-.99721 .74675e-1] +[.23713 -.97148] +[1.2343 -.46151e-1] +[-.74675e-1 -.37917] +[-.42533 -.54163] +[.18819 -.66246] +[.26287 1.3347] +[-.25731e-1 -.68819] +[.68819 -1.0257] +[-1.3507 -.16246] +[-.92533 .37917] +[.64656 .76287] +[-1.1597 .42533] +[-.35065 -.16246] +[-.16246 1.3507] +[-.85065 -.52573] +[.97148 .23713] +[-1.2343 -.57188] +[-1.2343 .46151e-1] +[.42533 1.1597] +[-.33754 1.1882] +[.85065 .52573] +[1.2343 .57188] +[-.42533 -1.1597] +[-.23713 .97148] +[1.1597 -.42533] +[.26287 -.28329] +[.38369 .46151e-1] +[-.18819 .66246] +[-.26287 .28329] +[1.0257 .68819] +[.30902 .95106] +[-.23713 -.64656] +[.16246 -1.3507] +[-.52573 .85065] +[.64656 -.23713] +[-1.1882 -.33754] +[.30902 -.95106] +[-1.0000 0] +[-.58779 .80902] +[0 1.0000] +[1.0000 0] +[.95106 -.30902] +[-.95106 -.30902] +[-.92533 .99721] +[.66246 1.1882] +[-1.1882 .66246] +[.97148 -.76287] +[-.26287 -1.3347] +[.80902 .58779] +[.38369 -.57188] +[.16246 -.35065] +[.18819 .33754] +[-.38369 -.46151e-1] +[1.1882 -.66246] +[.33754 -1.1882] +[-.37917 .74675e-1] +[.46151e-1 1.2343] +[.42533 .54163] +[-.46151e-1 .38369] +[-.46151e-1 -1.2343] +[-.68819 .25731e-1] +[-.80902 .58779] +[.80902 -.58779] +[-.30902 -.95106] +[.58779 -.80902] +[-.80902 -.58779] +[0 -1.0000] +[-.58779 -.80902] +[-.95106 .30902] +[-.30902 .95106] +[.58779 .80902] +[.95106 .30902] +] def +/NbrCells 120 def +/NbrEdges 720 def +/NbrVerticesInAnEdge 2 def +} def 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 diff --git a/Master/texmf-dist/tex/latex/pst-cox/pst-coxcoor.sty b/Master/texmf-dist/tex/latex/pst-cox/pst-coxcoor.sty new file mode 100644 index 00000000000..fc6ad1eef58 --- /dev/null +++ b/Master/texmf-dist/tex/latex/pst-cox/pst-coxcoor.sty @@ -0,0 +1,35 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% polygonesCoordinate\pst-coxcoor.sty +% Authors: J.-G. Luque and M. Luque +% Purpose: .sty file for the library pst-coxcoor +% 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/>. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\RequirePackage{pstricks} + \ProvidesPackage{pst-coxcoor}[2007/09/12 +package wrapper for + pst-coxcoor.tex (JG.L)] +\input{pst-coxcoor.tex} +\ProvidesFile{pst-coxcoor.tex} + [\filedate\space v\fileversion\space `PST-coxcoor' (JG.L)] +\endinput diff --git a/Master/texmf-dist/tex/latex/pst-cox/pst-coxeterp.sty b/Master/texmf-dist/tex/latex/pst-cox/pst-coxeterp.sty new file mode 100644 index 00000000000..c248c80870d --- /dev/null +++ b/Master/texmf-dist/tex/latex/pst-cox/pst-coxeterp.sty @@ -0,0 +1,34 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% pst-coxeter_parameter\pst-coxeterp.sty +% Authors: J.-G. Luque and M. Luque +% Purpose: .sty file for pst-coxeterp +% Created: 02/02/2008 +% License: LGPL +% Project: PSCox +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% 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/>. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\RequirePackage{pstricks} \ProvidesPackage{pst-coxeterp}[2007/09/12 +package wrapper for + pst-coxeterp.tex (JG.L)] +\input{pst-coxeterp.tex} +\ProvidesFile{pst-coxeterp.tex} + [\filedate\space v\fileversion\space `PST-coxeterp' (JG.L)] +\endinput |