From e1a7798f45cd37c0aa0bfaaef5f0acb4e48bc867 Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Fri, 22 Jan 2021 03:00:46 +0000 Subject: CTAN sync 202101220300 --- .../NamedGraphs/doc/latex/NamedGraphs-Platonic.tex | 338 --------------------- 1 file changed, 338 deletions(-) delete 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 deleted file mode 100644 index a29fcf126b..0000000000 --- a/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Platonic.tex +++ /dev/null @@ -1,338 +0,0 @@ -%!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