The icositruncated dodecadodecahedral graph is a cubic graph on 120 vertices and 180 edges that is the skeleton of the icositruncated dodecadodecahedron. It is illustrated above in a number of embeddings.
The icositruncated dodecadodecahedral graph is implemented in the Wolfram Language as GraphData["IcositruncatedDodecadodecahedralGraph"].
It is a bipartite graph, Cayley graph, Hamiltonian graph, unit-distance graph, and vertex-transitive graph.
