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]
| Name | Graph | 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 |