The ditrigonal icosidodecahedral graph is the skeleton of the cube 5-compound, ditrigonal dodecadodecahedron, great ditrigonal icosidodecahedron, and small ditrigonal icosidodecahedron.
It is Hamiltonian with 6,763,872 Hamiltonian cycles.
It is implemented in the Wolfram Language as GraphData["DitrigonalIcosidodecahedralGraph"].
