%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    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{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]
 \CoxeterC