\documentclass[11pt]{article}
\usepackage[latin1]{inputenc}%
\usepackage[a4paper]{geometry}
\usepackage{pst-coxeterp}
\usepackage{pst-coxcoor}
\usepackage[garamond]{mathdesign}
\renewcommand{\ttdefault}{lmtt}
\pagestyle{empty}
\begin{document}
{\tt PST-Cox} is a  {\tt LaTeX} library for drawing 2D projections
of regular complex polytopes. The regular complex polytopes are
hyperplans arrangements
 with some constraints whose automorphisms groups are generated by pseudo-reflections (complex reflections).
 They generalize the classical Platon solids.
In the following example, the complex polytopes $\beta_3^2$ and
$\beta_6^2$ are drawn. Their edges are respectively triangular and
hexagonal.
\begin{center}
\psset{unit=1.5}
\begin{pspicture}(-2,-2)(2,2)
 \psframe*(-2,-2)(2,2)
\gammaptwo[P=3,linecolor=white,sizeVertices=0.05,sizeCenters=0.05]
\end{pspicture}
\begin{pspicture}(-2,-2)(2,2)
\psframe*(-2,-2)(2,2)
\gammaptwo[P=6,linecolor=white,sizeVertices=0.05,sizeCenters=0.05]
\end{pspicture}
\end{center}
The regular complex polytope are related to the study of the roots
systems and are used in Mathematics as well as in Physics. For
example, some degenerate cases of the ternary trilinear forms admits
normal form which are the vertices of an Hessian polytope (regular
complex polytope in dimension $3$)
\[
\begin{pspicture}(-4,-3)(4,3)
\psset{unit=1.5cm,linewidth=0.01mm}
\CoxeterCoordinates[choice=9] %
\end{pspicture}
\]
Its group of automorphisms is a subgroup of order 648 of the Mashke
group which has been considered in the study of the $27$ lines of a
general cubic plane in $\mathbb P^3$. This polytope have been
considered by one of the author of the Library  in collaboration
with E. Briand, J.-Y. Thibon and F. Verstraete in the study of the
normal form of the three-qubit systems.
\end{document} 