SoccerBallGraph() creates the soccer ball graph on 60 vertices, also known as the truncated icosahedron graph, the buckminsterfullerene graph, or the buckyball graph. This is a planar 3-regular graph with no triangles.

SmallRhombicosidodecahedronGraph() creates the small rhombicosidodecahedron graph 60 vertices. This is a planar 4-regular Eulerian graph.

SnubDodecahedronGraph() creates the snub dodecahedron graph on 60 vertices. This is a planar 5-regular graph.

TruncatedDodecahedronGraph() creates the truncated dodecahedron graph on 60 vertices. This is a planar 3-regular graph.

All of these are Archimedean graphs.

You can optionally input the labels of the vertices as a list for any of the above graphs.

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

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

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

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

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

$\mathrm{true}$

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

$32$

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

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

The GraphTheory[SpecialGraphs][SmallRhombicosidodecahedronGraph], GraphTheory[SpecialGraphs][SnubDodecahedronGraph], GraphTheory[SpecialGraphs][TruncatedDodecahedronGraph] and GraphTheory[SpecialGraphs][TruncatedIcosahedronGraph] commands were introduced in Maple 2024.

For more information on Maple 2024 changes, see Updates in Maple 2024.