The triakis tetrahedral graph is Archimedean dual graph which is the skeleton of the triakis tetrahedron. It is the graph square of the 4-sunlet graph. It is a 3-tree.
It is implemented in the Wolfram Language as GraphData["TriakisTetrahedralGraph"].
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 | 24 |
| characteristic polynomial |  |
| chromatic number | 4 |
| chromatic polynomial |  |
| claw-free | no |
| clique number | 4 |
| determined by spectrum | yes |
| diameter | 2 |
| distance-regular graph | no |
| dual graph name | truncated tetrahedral graph |
| edge chromatic number | 6 |
| edge connectivity | 3 |
| edge count | 18 |
| Eulerian | no |
| girth | 3 |
| Hamiltonian | yes |
| Hamiltonian cycle count | 12 |
| Hamiltonian path count | 456 |
| integral graph | no |
| independence number | 4 |
| line graph | no |
| perfect matching graph | no |
| planar | yes |
| polyhedral graph | yes |
| polyhedron embedding names | triakis tetrahedron |
| radius | 2 |
| regular | no |
| square-free | no |
| traceable | yes |
| triangle-free | no |
| vertex connectivity | 3 |
| vertex count | 8 |
