The DuererGraph() command constructs the Dürer graph, a planar cubic graph with 12 vertices and 18 edges.

It is derived from Dürer's solid, a polyhedron first seen in an engraving by Albrecht Dürer.

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

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

$G≔\mathrm{DuererGraph}\left(\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 12\; vertices\; and\; 18\; edge(s)}$

$\mathrm{IsPlanar}\left(G\right)$

$\mathrm{true}$

$\mathrm{ChromaticNumber}\left(G\right)$

$3$

$\mathrm{Diameter}\left(G\right)$

$4$

$\mathrm{GroupTheory}:-\mathrm{GroupOrder}\left(\mathrm{AutomorphismGroup}\left(G\right)\right)$

$12$

$\mathrm{DrawGraph}\left(G\right)$

"Dürer graph", Wikipedia. http://en.wikipedia.org/wiki/Duerer_graph

The GraphTheory[SpecialGraphs][DuererGraph] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.