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Graph with an Archimedean solid as its skeleton From Wikipedia, the free encyclopedia
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]
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 |
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