\newpage\section{Tutte-Coxeter}\label{tutte} %<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> %<–––––––––––––––––––– Tutte –––––––––––––––––––––––––––––––> %<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> \begin{NewMacroBox}{grTutteCoxeter}{\oarg{options}} \medskip From MathWord : \url{http://mathworld.wolfram.com/LeviGraph.html} \emph{The Levi graph is the unique (3,8)-cage graph and Moore graph. It is also distance-regular and is also called the Tutte-Coxeter graph or Tutte's 8-cage.} \href{http://mathworld.wolfram.com/topics/GraphTheory.html}% {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% {\textcolor{blue}{E.Weisstein}} \medskip From Wikipedia : \url{http://en.wikipedia.org/wiki/Tutte–Coxeter_graph} \emph{In the mathematical field of graph theory, the Tutte–Coxeter graph or Tutte eight-cage is a 3-regular graph with 30 vertices and 45 edges. As the unique smallest cubic graph of girth 8 it is a cage and a Moore graph. It is bipartite, and can be constructed as the Levi graph of the generalized quadrangle. The graph is named after William Thomas Tutte and H. S. M. Coxeter; it was discovered by Tutte (1947) but its connection to geometric configurations was investigated by both authors in a pair of jointly published papers (Tutte 1958; Coxeter 1958a).} \end{NewMacroBox} \subsection{\tkzname{Tutte-Coxeter graph (3,8)-cage or Levi graph}} An other method to get the same result is~: \medskip \begin{tkzexample}[code only] \grLCF[RA=7]{-13,-9,7,-7,9,13}{5}\end{tkzexample} \bigskip \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture}[scale=.7] \GraphInit[vstyle=Art] \tikzset{VertexStyle/.append style={minimum size=2pt}} \SetGraphArtColor{blue}{darkgray} \grTutteCoxeter \end{tikzpicture} \end{tkzexample} \end{center} \endinput