Disdyakis Dodecahedral Graph

The disdyakis dodecahedral graph is an 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 matrices, incidence matrices, and graph distance matrices for the disdyakis dodecahedral 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