# 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 Graph Degree Edges Vertices Order
truncated tetrahedral graph3181224
cuboctahedral graph4241248
truncated cubical graph3362448
truncated octahedral graph3362448
rhombicuboctahedral graph4482448
truncated cuboctahedral graph
(great rhombicuboctahedron)
3724848
snub cubical graph5602424
icosidodecahedral graph46030120
truncated dodecahedral graph39060120
truncated icosahedral graph39060120
rhombicosidodecahedral graph412060120
truncated icosidodecahedral graph
(great rhombicosidodecahedron)
3180120120
snub dodecahedral graph51506060