Archimedean graph

In the mathematical field of graph theory, an Archimedean graph is a graph that forms the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, and all of them are regular, polyhedral (and therefore by necessity also 3-vertex-connected planar graphs), and also Hamiltonian graphs.[1]

Along with the 13, the set of infinite prism graphs and antiprism graphs can also be considered Archimedean graphs.[2]

Graph elements
Name	Degree	Edges	Vertices	Order
truncated tetrahedral graph	3	18	12	24
cuboctahedral graph	4	24	12	48
truncated cubical graph	3	36	24	48
truncated octahedral graph	3	36	24	48
rhombicuboctahedral graph	4	48	24	48
truncated cuboctahedral graph (great rhombicuboctahedron)	3	72	48	48
snub cubical graph	5	60	24	24
icosidodecahedral graph	4	60	30	120
truncated dodecahedral graph	3	90	60	120
truncated icosahedral graph	3	90	60	120
rhombicosidodecahedral graph	4	120	60	120
truncated icosidodecahedral graph (great rhombicosidodecahedron)	3	180	120	120
snub dodecahedral graph	5	150	60	60