The snub dodecahedral graph is a quintic graph on 60 nodes and 150 edges that corresponds to the skeleton of the snub dodecahedron, great inverted snub icosidodecahedron, great retrosnub icosidodecahedron, and great snub icosidodecahedron.
The snub dodecahedral graph is planar and Hamiltonian, and has chromatic number 4. It is vertex-transitive, although not edge-transitive because some edges are part of three-circuits while others are not.
It is implemented in the Wolfram Language as GraphData["SnubDodecahedralGraph"].
