A quartic symmetric graph on 30 nodes and 60 edges corresponding to the skeleton of the Archimdean icosidodecahedron, great dodecahemidodecahedron, great icosidodecahedron, great icosihemidodecahedron, small dodecahemidodecahedron, and small icosihemidodecahedron. It is illustrated above in a number of symmetrical embeddings.
It has a total of 
distinct (directed) Hamiltonian
cycles, which yield two inequivalent order-6 generalized LCF
notations, one of order 3, two of order 2, and 649 of order 1. The LCF embeddings
of order greater than one are illustrated above.
It has graph diameter 5, graph radius 5, and chromatic number 3. Its graph
spectrum is 
.
It is the line graph of the dodecahedral graph.
