# How to draw the Errera's graph

someone could you give me an example to draw this graph? My difficulty is set lengths in each vertex, I use tkz-graph

# Uncompleted example

\documentclass[tikz]{standalone}
\usepackage{tkz-graph}
\begin{document}
\begin{tikzpicture}
\SetGraphUnit{2}
\GraphInit[vstyle=Classic]
\SetVertexNoLabel
\Vertex[x=0, y=0]{v1}
\Vertex[x=10,y=0]{v2}
\Vertex[x=5,y=0.5]{v3}
\Edges(v1,v2,v3,v1)
\Vertex[x=2.5,y=1]{v4}
\Vertex[x=7.5,y=1]{v5}
\Edges(v3,v4,v5,v3)
\Vertex[x=4,y=1.5]{v6}
\Vertex[x=8,y=1.5]{v7}
%Continue ...
\end{tikzpicture}
\end{document}


I think that there is another way to draw

All suggestions are welcome.

Thanks!

• Did you check the graphdrawing library of TikZ in the manual? – percusse Jun 22 '18 at 0:18
• @percusse I am not sure if the algorithms of the graphdrawing library are able to deal with an Errera graph, but I might be wrong. – user121799 Jun 22 '18 at 0:54
• Thanks @percusse, I found a presentation and a nice article of Graph Drawing in TikZ by Till Tantau and a poster from Graph Drawing and Network Visualization :) – Oromion Jun 22 '18 at 1:52

Luckily Mathematica has the graph data. Unfortunately, my French is practically nonexistent, so I cannot appreciate the benefits of that package.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tkz-graph}
\begin{document}
\begin{tikzpicture}
\SetGraphUnit{2}
\GraphInit[vstyle=Classic]
\SetVertexNoLabel
\foreach \X/\Y [count=\Z] in {4/ 13, 4/ 6, -0.2/ 5, 2/ 2.2, -6/ -1, 6/ 2.2,
9.5/ 1.6, 2.7/ 5, 4.8/ 7.8, 4/ 10.4, -1.5/ 1.6, 14/ -1, 4/ 3.6,
5.3/ 5, 3.2/ 7.8, 4/ 0.3, 8.1/ 5}
{\Vertex[x=\X,y=\Y]{v\Z}}
\Edges(v2,v8,v13,v14,v2)
\Edges(v5,v12,v16,v5)
\Edges(v5,v11,v16,v7,v12)
\Edges(v11,v4,v16,v6,v7)
\Edges(v4,v8,v15,v10,v9,v14,v6)
\Edges(v4,v13,v6,v4)
\Edges(v13,v2,v15,v9,v2)
\Edges(v3,v10,v17)
\Edges(v11,v15,v3)
\Edges(v7,v9,v17)
\Edges(v5,v3,v11)
\Edges(v12,v17,v7)
\Edges(v5,v1,v12)
\Edges(v3,v1,v17)
\Edges(v1,v10)
\Edges(v11,v8)
\Edges(v7,v14)
\end{tikzpicture}
\end{document}


• Ingenious answer, @marmot please could you show how you got that data (if it's in Mathematica commands), I would also like to get your graphs from Solfer, Heawood. I think Mathematica has something similar to doc.sagemath.org/html/en/reference/graphs/sage/graphs/… – Oromion Jun 22 '18 at 3:02
• @Oromion Here is the link to the Mathematica notebook. I just typed GraphData["ErreraGraph"] // InputForm and used a regex c & p to convert the vertices to the list in \foreach, and the edges I drew by hand because I figured that understanding the Mathematica syntax for that may take longer. – user121799 Jun 22 '18 at 3:10
• Fantastic, thank you so much, it works :) i.imgur.com/qbMWTCF.png – Oromion Jun 22 '18 at 3:35