Archimedean Graph

A graph corresponding to the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, all of which are regular, planar, polyhedral, and Hamiltonian.

The following table lists the Archimedean graphs , their connectivity , number of vertices , number of edges , order of the automorphism group, Hamiltonicity, Eulerianicity, vertex-transitivity, and edge-transitivity. Note that all Archimedean graphs are Hamiltonian, vertex-transitive.

graph	connectivity				Hamiltonian	Eulerian	vertex-transitive	edge-transitive
cuboctahedral graph	quartic	12	24	48	yes	yes	yes	yes
great rhombicosidodecahedral graph	cubic	120	180	120	yes	no	yes	no
great rhombicuboctahedral graph	cubic	48	72	48	yes	no	yes	no
icosidodecahedral graph	quartic	30	60	120	yes	yes	yes	yes
small rhombicosidodecahedral graph	quartic	60	120	120	yes	yes	yes	no
small rhombicuboctahedral graph	quartic	24	48	48	yes	yes	yes	no
snub cubical graph	quintic	24	60	24	yes	no	yes	no
snub dodecahedral graph	quintic	60	150	60	yes	no	yes	no
truncated cubical graph	cubic	24	36	48	yes	no	yes	no
truncated dodecahedral graph	cubic	60	90	120	yes	no	yes	no
truncated icosahedral graph	cubic	60	90	120	yes	no	yes	no
truncated octahedral graph	cubic	24	36	48	yes	no	yes	no
truncated tetrahedral graph	cubic	12	18	24	yes	no	yes	no