%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 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 . % \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}