From 877268a0de707a979be934d888518f6cc02d73a6 Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Tue, 10 Mar 2020 03:01:27 +0000 Subject: CTAN sync 202003100301 --- .../NamedGraphs/doc/latex/NamedGraphs-Platonic.tex | 338 +++++++++++++++++++++ 1 file changed, 338 insertions(+) create mode 100644 obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Platonic.tex (limited to 'obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Platonic.tex') 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 new file mode 100644 index 0000000000..a29fcf126b --- /dev/null +++ b/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Platonic.tex @@ -0,0 +1,338 @@ +%!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 -- cgit v1.2.3