The SoccerBallGraph command creates the so called soccer ball graph on 60 vertices. The soccer ball graph is a planar 3-regular graph with no triangles. As an option, you may input the labels of the vertices as a set or list of size 60.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$\mathrm{SB}≔\mathrm{SoccerBallGraph}\left(\right)$

$\mathrm{SB}≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 60\; vertices\; and\; 90\; edge(s)}$

$\mathrm{IsPlanar}\left(\mathrm{SB}\,'F'\right)$

$\mathrm{true}$

$\mathrm{nops}\left(F\right)$

$32$

$\mathrm{DrawGraph}\left(\mathrm{SB}\,\mathrm{style}=\mathrm{spring}\right)$

$\mathrm{DrawGraph}\left(\mathrm{SB}\,\mathrm{style}=\mathrm{spring}\,\mathrm{dimension}=3\right)$