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\newpage\section{Coxeter}
%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<––––––––––––––––––––––––––––– Coxeter ––––––––––––––––––––––––––––––––>
%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
From MathWorld : \url{http://mathworld.wolfram.com/CoxeterGraph.html}
The Coxeter graph is a nonhamiltonian cubic symmetric graph on 28 vertices and 42 edges.
\subsection{\tkzname{Coxeter graph I}}
\bigskip
\begin{center}
\begin{tkzexample}[vbox]
\begin{tikzpicture}[rotate=90,scale=1]
\GraphInit[vstyle=Art]
\SetGraphArtColor{magenta}{gray}
\grCycle[RA=5,prefix=a]{7}
\begin{scope}[rotate=-20]\grEmptyCycle[RA=4,prefix=b]{7}\end{scope}
\grCirculant[RA=3,prefix=c]{7}{2}
\grCirculant[RA=1.4,prefix=d]{7}{3}
\EdgeIdentity{a}{b}{7}
\EdgeIdentity{b}{c}{7}
\EdgeIdentity{b}{d}{7}
\end{tikzpicture}
\end{tkzexample}
\end{center}
\vfill\newpage
\subsection{\tkzname{Coxeter graph II}}
\bigskip
\begin{center}
\begin{tkzexample}[vbox]
\begin{tikzpicture}
\GraphInit[vstyle=Art]
\SetGraphArtColor{magenta}{gray}
\grCycle[RA=7,prefix=b]{24}
\grEmptyStar[RA=3,prefix=a]{4}
\EdgeDoubleMod{a}{3}{0}{1}{b}{24}{0}{8}{2}
\EdgeDoubleMod{a}{3}{0}{1}{b}{24}{7}{8}{2}
\EdgeDoubleMod{a}{3}{0}{1}{b}{24}{18}{8}{2}
\EdgeDoubleMod{a}{4}{3}{0}{b}{24}{22}{8}{2}
\EdgeInGraphMod*{b}{24}{6}{5}{8}
\EdgeInGraphMod*{b}{24}{11}{1}{8}
\end{tikzpicture}
\end{tkzexample}
\end{center}
\vfill\newpage
\subsection{\tkzname{Coxeter graph III}}
\bigskip
\begin{center}
\begin{tkzexample}[vbox]
\begin{tikzpicture}
\GraphInit[vstyle=Art]
\SetGraphArtColor{magenta}{gray}
\grCycle[RA=7,prefix=c]{7}
\grEmptyCycle[RA=6,prefix=b]{7}
\begin{scope}[rotate=12.85]\grEmptyCycle[RA=5,prefix=a]{14}\end{scope}
\EdgeIdentity{b}{c}{7}
\EdgeDoubleMod{b}{7}{0}{1}{a}{14}{0}{2}{6}
\EdgeDoubleMod{b}{7}{0}{1}{a}{14}{13}{2}{6}
\EdgeInGraphModLoop{a}{14}{4}{0}{0}
\EdgeInGraphModLoop{a}{14}{6}{1}{1}
\end{tikzpicture}
\end{tkzexample}
\end{center}
%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––– Tutte-Coxeter graph ––––––––––––––––––––––––––––>
%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\vfill\newpage
\subsection{\tkzname{Tutte-Coxeter graph I}}
\tikzstyle{VertexStyle} = [very thin,draw,
shape = circle,
color = white,
fill = black,
inner sep = 0pt,
minimum size = 18pt]
\tikzstyle{EdgeStyle} = [thick,
double = brown,
double distance = 1pt]
\bigskip
\begin{center}
\begin{tkzexample}[vbox]
\begin{tikzpicture}[scale=3]
\GraphInit[vstyle=Art]
\SetGraphArtColor{blue}{cyan}
\begin{scope}[rotate=5]\grCycle[RA=2.5,prefix=a]{10}\end{scope}
\begin{scope}[rotate=-10]\grCirculant[RA=1.8,prefix=b]{10}{5}\end{scope}
\begin{scope}[rotate=36]\grCirculant[RA=1.1,prefix=c]{10}{3}\end{scope}
\EdgeIdentity{a}{b}{10}
\EdgeIdentity{b}{c}{10}
\end{tikzpicture}
\end{tkzexample}
\end{center}
%
\vfill\newpage
\subsection{\tkzname{Tutte-Coxeter graph II}}
\bigskip
\begin{center}
\begin{tkzexample}[vbox]
\begin{tikzpicture}
\GraphInit[vstyle=Art]
\SetGraphArtColor{blue}{darkgray}
\grLCF[RA=7]{-13,-9,7,-7,9,13}{5}
\end{tikzpicture}
\end{tkzexample}
\end{center}
\endinput
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