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 also Hamiltonian graphs.
Along with the 13, the set of infinite prism graphs and antiprism graphs can also be considered Archimedean graphs.
| 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 | 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 | 3 | 180 | 120 | 120 | |
| snub dodecahedral graph | 5 | 150 | 60 | 60 |