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.An Atlas of Graphs, p. 267-270
Along with the 13, the infinite sets of prism graphs and antiprism graphs can also be considered Archimedean graphs.An Atlas of Graphs, p. 261
+ Graph elements NameGraph Degree Edges Vertices Automorphisms truncated tetrahedral graph3 18 1224 cuboctahedral graph4 24 1248 truncated cubical graph3 36 2448 truncated octahedral graph3 36 2448 rhombicuboctahedral graph4 48 2448 truncated cuboctahedral graph(great rhombicuboctahedron)3 72 4848 snub cubical graph5 60 2424 icosidodecahedral graph4 60 30120 truncated dodecahedral graph3 90 60120 truncated icosahedral graph3 90 60120 rhombicosidodecahedral graph4 120 60120 truncated icosidodecahedral graph(great rhombicosidodecahedron)3 180 120120 snub dodecahedral graph5 150 6060
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