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 infinite sets of prism graphs and antiprism graphs can also be considered Archimedean graphs.^[2]

Graph elements

Name	Graph	Degree	Edges	Vertices	Automorphisms
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

See also

• Platonic graph
• Wheel graph