From 877268a0de707a979be934d888518f6cc02d73a6 Mon Sep 17 00:00:00 2001
From: Norbert Preining <norbert@preining.info>
Date: Tue, 10 Mar 2020 03:01:27 +0000
Subject: CTAN sync 202003100301

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 .../NamedGraphs/doc/latex/NamedGraphs-Platonic.tex | 338 +++++++++++++++++++++
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diff --git a/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Platonic.tex b/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Platonic.tex
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+%!TEX root = /Users/ego/Boulot/TKZ/tkz-berge/NamedGraphs/doc/NamedGraphs-main.tex
+\newpage\section{ The five Platonics Graphs}
+%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
+%<––––––––––––––––––––  Platonic graphs      –––––––––––––––––––––––––––––––>
+%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
+
+The Platonic Graphs are the graphs formed by the edges and vertices of the five regular Platonic solids. The five Platonics Graphs  are illustrated below.  
+
+\begin{enumerate}
+  \item tetrahedral
+  \item octahedral
+  \item cube
+  \item icosahedral
+  \item dodecahedral
+\end{enumerate} 
+
+
+%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
+%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
+\begin{NewMacroBox}{grTetrahedral}{\oarg{RA=Number}}
+From MathWord : \url{http://mathworld.wolfram.com/TetrahedralGraph.html} 
+
+\emph{\tkzname{Tetrahedral Graph}  is the unique polyhedral graph on four nodes which is also the complete graph  and therefore also the wheel graph . It is implemented as \tkzcname{grTetrahedral}}
+\href{http://mathworld.wolfram.com/TetrahedralGraph.html}%
+           {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}%
+           {\textcolor{blue}{E.Weisstein}
+}
+It has :
+
+\begin{enumerate}
+ \item  4 nodes,
+ \item  6 edges,
+ \item  graph diameter 1.
+\end{enumerate}
+
+The  Tetrahedral Graph is 3-Regular
+\end{NewMacroBox}
+
+\subsection{\tkzname{Tetrahedral}}
+\begin{center}
+\begin{tkzexample}[vbox]
+\begin{tikzpicture}[scale=.6]
+      \GraphInit[vstyle=Shade]
+      \renewcommand*{\VertexInnerSep}{4pt} 
+      \SetVertexNoLabel\SetGraphShadeColor{red!50}{black}{red}
+      \grTetrahedral[RA=5]
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\clearpage\newpage
+\subsection{\tkzname{Tetrahedral LCF embedding}}
+
+\vspace*{2cm}
+\begin{center}
+  \begin{tkzexample}[vbox]
+\begin{tikzpicture}[rotate=18]
+     \renewcommand*{\VertexInnerSep}{8pt} 
+     \GraphInit[vstyle=Art]
+     \SetGraphArtColor{red!50}{orange}
+     \grLCF[RA=7]{2,-2}{2}
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\clearpage\newpage   
+%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
+%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
+
+\begin{NewMacroBox}{grOctahedral}{\oarg{RA=\meta{Number},RB=\meta{Number}}}
+
+\medskip
+From MathWord : \url{http://mathworld.wolfram.com/OctahedralGraph.html} 
+
+\emph{\tkzname{Octahedral Graph}  is isomorphic to the circulant graph $CI_{[1,2]}(6)$ . Two embeddings of this graph are illustrated below. It is implemented as \tkzcname{grOctahedral} or as \tkzcname{grSQCycle\{6\}}.}
+\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}}   
+
+It has :
+
+\begin{enumerate}
+ \item  6 nodes,
+ \item  12 edges,
+ \item  graph diameter 2.
+\end{enumerate}
+
+\medskip
+ The  Octahedral Graph is 4-Regular.
+\end{NewMacroBox}
+
+
+\medskip
+\subsection{\tkzname{Octahedral}}
+\begin{center}
+\begin{tkzexample}[vbox]
+\begin{tikzpicture}
+  \grOctahedral[RA=6,RB=2]
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\vfill\newpage\null
+\begin{center}
+\begin{tkzexample}[vbox]
+\begin{tikzpicture}
+       \grSQCycle[RA=5]{6}
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\vfill\newpage\null
+%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
+%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
+
+\medskip
+\begin{NewMacroBox}{grCubicalGraph}{\oarg{RA=\meta{Number},RB=\meta{Number}}}
+
+\medskip
+From MathWord : \url{http://mathworld.wolfram.com/CubicalGraph.html} 
+
+\emph{\tkzname{Cubical Graph}  is isomorphic to a generalized Petersen graph  $PG_{[4,1]}$, to a bipartite Kneser graph , to a crown graph and it is equivalent to the Cycle Ladder $CL(4)$. Two embeddings of this graph are illustrated below. It is implemented as \tkzcname{grCubicalGraph} or \tkzcname{grPrism\{4\}}.}
+\href{http://mathworld.wolfram.com/CubicalGraph.html}%
+           {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}%
+           {\textcolor{blue}{E.Weisstein}}
+
+It has :
+
+\begin{enumerate}
+ \item  8 nodes,
+ \item  12 edges,
+ \item  graph diameter 3.
+\end{enumerate}
+
+ The  Cubical Graph is 3-Regular.
+\end{NewMacroBox}
+
+\subsection{\tkzname{Cubical Graph : form 1}}
+\begin{center}
+  \begin{tkzexample}[vbox]
+\begin{tikzpicture}
+  \grCubicalGraph[RA=5,RB=2]
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\vfill\newpage\null 
+\subsection{\tkzname{Cubical Graph : form 2}}
+\begin{center}
+  \begin{tkzexample}[vbox]
+\begin{tikzpicture}
+  \grCubicalGraph[form=2,RA=7,RB=4]
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\vfill\newpage
+\subsection{\tkzname{Cubical LCF embedding}}
+
+\vspace*{2cm}
+\begin{center}
+\begin{tkzexample}[vbox]
+\begin{tikzpicture}[rotate=18]
+    \GraphInit[vstyle=Art]\renewcommand*{\VertexInnerSep}{8pt} 
+    \SetGraphArtColor{red!50}{orange}
+    \grLCF[RA=7]{3,-3}{4}
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\clearpage\newpage
+%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
+
+\begin{NewMacroBox}{grIcosahedral}{\oarg{RA=\meta{Number},RB=\meta{Number},RC=\meta{Number}}}
+
+\medskip
+From MathWord : \url{http://mathworld.wolfram.com/IcosahedralGraph.html} 
+
+\emph{The \tkzname{Icosahedral Graph}  is the Platonic graph whose nodes have the connectivity of the icosahedron, illustrated above in a number of embeddings. The icosahedral graph has 12 vertices and 30 edges. Since the icosahedral graph is regular and Hamiltonian, it has a generalized LCF notation.}
+\href{http://mathworld.wolfram.com/IcosahedralGraph.html}%
+           {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}%
+           {\textcolor{blue}{E.Weisstein}}
+
+\medskip
+It has :
+
+\begin{enumerate}
+ \item  12 nodes,
+ \item  30 edges,
+ \item  graph diameter 3.
+\end{enumerate}
+
+\medskip
+ The  Icosahedral Graph is 5-Regular.
+\end{NewMacroBox}
+
+\medskip
+
+\subsection{\tkzname{Icosahedral forme 1 }}
+
+\tikzstyle{EdgeStyle}= [thick,%
+                        double          = orange,%
+                        double distance = 1pt] 
+
+\begin{center}
+\begin{tkzexample}[vbox]
+\begin{tikzpicture}[scale=.8]
+ \GraphInit[vstyle=Art]\renewcommand*{\VertexInnerSep}{4pt} 
+ \SetGraphArtColor{red}{orange}
+ \grIcosahedral[RA=5,RB=1]
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\clearpage\newpage    
+
+\subsection{\tkzname{Icosahedral forme 2 }}
+\vspace*{2cm}
+\begin{center}
+\begin{tkzexample}[vbox]
+\begin{tikzpicture}[rotate=-30]
+   \GraphInit[vstyle=Art]  \renewcommand*{\VertexInnerSep}{8pt} 
+   \SetGraphArtColor{red!50}{orange}
+   \grIcosahedral[form=2,RA=8,RB=2,RC=.8]
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\vfill\newpage
+
+\subsection{\tkzname{Icosahedral} \tkzname{RA=1} et \tkzname{RB=7}}
+\begin{center}
+\begin{tkzexample}[vbox]
+ \begin{tikzpicture}
+    \GraphInit[vstyle=Art]  \renewcommand*{\VertexInnerSep}{8pt} 
+    \SetGraphArtColor{red!50}{orange}
+    \grIcosahedral[RA=1,RB=7]
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\clearpage\newpage    
+\subsection{\tkzname{Icosahedral LCF embedding 1}}
+
+\vspace*{2cm}
+\begin{center}
+\begin{tkzexample}[vbox]
+\begin{tikzpicture}[rotate=18]
+    \GraphInit[vstyle=Art]  \renewcommand*{\VertexInnerSep}{8pt} 
+    \SetGraphArtColor{red!50}{orange}
+    \grLCF[RA=7]{-4,-3,4}{6}
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\clearpage\newpage    
+\subsection{\tkzname{Icosahedral LCF embedding 2}}
+
+\vspace*{2cm}
+\begin{center}
+\begin{tkzexample}[vbox]
+\begin{tikzpicture}[rotate=18]
+   \GraphInit[vstyle=Art]
+   \SetGraphArtColor{red!50}{orange}
+   \grLCF[RA=7]{-2,2,3}{6}
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\clearpage\newpage 
+%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
+
+\begin{NewMacroBox}{grDodecahedral}{\oarg{RA=\meta{Number},RB=\meta{Number},RC=\meta{Number},RD=\meta{Number}}}
+
+\medskip
+From MathWord : \url{http://mathworld.wolfram.com/DodecahedralGraph.html} 
+
+\emph{The \tkzname{Icosahedral Graph}  is the Platonic graph corresponding to the connectivity of the vertices of a dodecahedron, illustrated above in four embeddings. The left embedding shows a stereographic projection of the dodecahedron, the second an orthographic projection, the third is from Read and Wilson, and the fourth is derived from LCF notation.}
+\href{http://mathworld.wolfram.com/DodecahedralGraph.html}%
+           {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}%
+           {\textcolor{blue}{E.Weisstein}}
+
+\medskip
+It has :
+
+\begin{enumerate}
+ \item  20 nodes,
+ \item  30 edges,
+ \item  graph diameter 5.
+\end{enumerate}
+
+\medskip
+ The  Dodecahedral Graph is 3-Regular.
+\end{NewMacroBox}
+
+\medskip
+\subsection{\tkzname{Dodecahedral}}
+
+\begin{center}
+\begin{tkzexample}[vbox]
+\begin{tikzpicture}[rotate=18,scale=.6]
+   \GraphInit[vstyle=Art]
+   \SetGraphArtColor{red!50}{orange}
+   \grDodecahedral[RA=7,RB=4,RC=2,RD=1]
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\subsection{\tkzname{Dodecahedral other embedding}}
+
+\vspace*{2cm}
+\begin{center}
+\begin{tkzexample}[vbox]
+\begin{tikzpicture}
+   \grCycle[RA=7,prefix=a]{10}
+   \grSQCycle[RA=4,prefix=b]{10}
+     \foreach \v in {0,...,9}
+       {\Edge(a\v)(b\v)}
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+\vfill\newpage
+\subsection{\tkzname{Dodecahedral LCF embedding}}
+
+\vspace*{2cm}
+\begin{center}
+\begin{tkzexample}[vbox]
+\begin{tikzpicture}[rotate=18]
+   \GraphInit[vstyle=Art]
+   \SetGraphArtColor{red!50}{orange}
+   \grLCF[RA=7]{10,7,4,-4,-7,10,-4,7,-7,4}{2}
+ \end{tikzpicture}
+\end{tkzexample} 
+\end{center}
+
+
+\endinput
-- 
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