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.

Along with the 13, the infinite sets of prism graphs and antiprism graphs can also be considered Archimedean graphs.

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

References

• Read, R. C. and Wilson, R. J. An Atlas of Graphs, Oxford, England: Oxford University Press, 2004 reprint, Chapter 6 special graphs pp. 261, 267–269.

External links

• Weisstein, Eric W. "Archimedean Graph". MathWorld.