The small rhombicosidodecahedral graph is a quartic graph on 60 nodes and 120 edges that corresponds to the skeleton of the small rhombicosidodecahedron, as well as the great dodecicosidodecahedron, great rhombidodecahedron, quasirhombicosidodecahedron, small dodecicosidodecahedron, small rhombicosidodecahedron, and small rhombidodecahedron uniform polyhedra.
It has graph diameter 8, graph radius 8, and chromatic number 3. It is also Hamiltonian. 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["SmallRhombicosidodecahedralGraph"].
