The GeneralizedHexagonGraph() command returns the generalized hexagon graph, also known as the Tutte 12-cage graph or the Benson graph.

It is the unique (3,12) cage graph.

The Tutte12CageGraph() command is an alias for GeneralizedHexagonGraph().

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

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

$G≔\mathrm{GeneralizedHexagonGraph}\left(\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 126\; vertices\; and\; 189\; edge(s)}$

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

$\mathrm{true}$

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

$12$

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

"Tutte 12-cage", Wikipedia. http://en.wikipedia.org/wiki/Tutte_12-cage

Benson, Clark Tabor. Minimal Regular Graphs of Girth 8 and 12. Can. J. Math. 18, 1091–1094, 1966. doi:10.4153/CJM-1966-109-8.