IsArchimedeanGraph(G) returns true if G is an Archimedean graph and false otherwise.

IsPlatonicGraph(G) returns true if G is an Platonic graph and false otherwise.

A Platonic graph is a graph that forms the graph skeleton of one of the Platonic solids. There are 5 Platonic graphs, and all of them are regular, polyhedral, planar, and Hamiltonian.

An Archimedean graph is a graph that forms the graph skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, and all of them are regular, polyhedral, planar, and Hamiltonian.

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

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

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

$\mathrm{SB}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 60\; vertices\; and\; 90\; edges}$

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

$\mathrm{true}$

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

$32$

$\mathrm{IsPlatonicGraph}\left(\mathrm{SB}\right)$

$\mathrm{false}$

$\mathrm{IsArchimedeanGraph}\left(\mathrm{SB}\right)$

$\mathrm{true}$

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

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

The GraphTheory[IsArchimedeanGraph] command was introduced in Maple 2024.

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

The GraphTheory[IsPlatonicGraph] command was introduced in Maple 2025.

For more information on Maple 2025 changes, see Updates in Maple 2025.