CuboctahedronGraph() creates the cuboctahedron graph on 12 vertices.

TruncatedTetrahedronGraph() creates the truncated tetrahedron graph on 12 vertices.

Both of these are Archimedean graphs.

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

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

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

$\mathrm{CG}≔\mathrm{CuboctahedronGraph}\left(\right)$

$\mathrm{CG}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 12\; vertices\; and\; 24\; edges}$

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

$\mathrm{true}$

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

$14$

$\mathrm{TTG}≔\mathrm{TruncatedTetrahedronGraph}\left(\right)$

$\mathrm{TTG}≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 12\; vertices\; and\; 18\; edges}$

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

$\mathrm{true}$

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

$8$

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

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

The GraphTheory[SpecialGraphs][CuboctahedronGraph] and GraphTheory[SpecialGraphs][TruncatedTetrahedronGraph] commands were introduced in Maple 2024.

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