The tetrakis hexahedral graph is Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as GraphData["TetrakisHexahedralGraph"].
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 | ? |
diameter | 3 |
distance-regular graph | no |
dual graph name | truncated octahedral graph |
edge chromatic number | 6 |
edge connectivity | 4 |
edge count | 36 |
Eulerian | yes |
girth | 3 |
Hamiltonian | yes |
Hamiltonian cycle count | 3408 |
Hamiltonian path count | ? |
integral graph | no |
independence number | 6 |
line graph | ? |
line graph name | ? |
perfect matching graph | no |
planar | yes |
polyhedral graph | yes |
polyhedron embedding names | tetrakis hexahedron |
radius | 3 |
regular | no |
square-free | no |
traceable | yes |
triangle-free | no |
vertex connectivity | 4 |
vertex count | 14 |