The deltoidal icositetrahedral graph is Archimedean dual graph which is the skeleton of the deltoidal icositetrahedron. It is implemented in the Wolfram Language as GraphData["DeltoidalIcositetrahedralGraph"].
The plots above show the adjacency, incidence, and graph distance matrices for the deltoidal icositetrahedral graph.
The following table summarizes some properties of the graph.
| property | value |
| automorphism group order | 48 |
| characteristic polynomial |  |
| chromatic number | 2 |
| chromatic polynomial | ? |
| claw-free | no |
| clique number | 2 |
| determined by spectrum | ? |
| diameter | 6 |
| distance regular | no |
| dual graph name | small rhombicuboctahedral graph |
| edge chromatic number | 4 |
| edge connectivity | 3 |
| edge count | 48 |
| Eulerian | no |
| girth | 4 |
| Hamiltonian | no |
| Hamiltonian cycle count | 0 |
| Hamiltonian path count | 0 |
| independence number | 14 |
| integral | no |
| line graph | ? |
| perfect matching graph | no |
| planar | yes |
| polyhedral graph | yes |
| radius | 4 |
| regular | no |
| square-free | no |
| traceable | no |
| triangle-free | yes |
| vertex connectivity | 3 |
| vertex count | 26 |
