The dodecicosahedral graph is the skeleton graph of the great ditrigonal dodecicosidodecahedron, great dodecicosahedron, great icosicosidodecahedron, small ditrigonal dodecicosidodecahedron, small dodecicosahedron, and small icosicosidodecahedron. It is illustrated above in a few embeddings.
It is implemented in the Wolfram Language as GraphData["DodecicosahedralGraph"].
