Archimedean Dual Graph

The 13 Archimedean dual graphs are the skeletons of the Archimedean dual solids, illustrated above. Since they are polyhedral graphs, they are also planar. However, none of them are regular.

The following table summarizes properties of the Archimedean dual graphs.

graph				Hamiltonian	Eulerian	vertex-transitive	edge-transitive
deltoidal hexecontahedral graph	62	120	120	no	no	no	no
deltoidal icositetrahedral graph	26	48	48	no	no	no	no
disdyakis dodecahedral graph	26	72	48	yes	yes	no	no
disdyakis triacontahedral graph	62	180	120	yes	yes	no	no
pentagonal hexecontahedral graph	92	150	60	yes	no	no	no
pentagonal icositetrahedral graph	38	60	24	yes	no	no	no
pentakis dodecahedral graph	32	90	120	yes	no	no	no
rhombic dodecahedral graph	14	24	48	no	no	no	yes
rhombic triacontahedral graph	32	60	120	no	no	no	yes
small triakis octahedral graph	14	36	48	no	no	no	no
tetrakis hexahedral graph	14	36	48	yes	yes	no	no
triakis icosahedral graph	32	90	120	no	no	no	no
triakis tetrahedral graph	8	18	24	yes	no	no	no