The disdyakis dodecahedral graph is Archimedean dual graph which is the skeleton of the disdyakis dodecahedron. It is implemented in the Wolfram Language as GraphData["DisdyakisDodecahedralGraph"].
The plots above show the adjacency, incidence, and graph distance matrices for the deltoidal hexecontahedral graph.
The following table summarizes some properties of the graph.
| property | value |
| automorphism group order | 48 |
| characteristic polynomial |  |
| chromatic number | 3 |
| chromatic polynomial | ? |
| claw-free | no |
| clique number | 3 |
| determined by spectrum | no |
| diameter | 4 |
| distance-regular graph | no |
| dual graph name | great rhombicuboctahedral graph |
| edge chromatic number | 8 |
| edge connectivity | 4 |
| edge count | 72 |
| Eulerian | yes |
| girth | 3 |
| Hamiltonian | yes |
| Hamiltonian cycle count | 697824 |
| Hamiltonian path count | ? |
| integral graph | no |
| independence number | 12 |
| line graph | ? |
| perfect matching graph | no |
| planar | yes |
| polyhedral graph | yes |
| polyhedron embedding names | disdyakis dodecahedron, Escher's solid |
| radius | 4 |
| regular | no |
| square-free | no |
| traceable | yes |
| triangle-free | no |
| vertex connectivity | 4 |
| vertex count | 26 |
