Archimedean graph

Short description: Graph with an Archimedean solid as its skeleton

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 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

## See also

* Platonic graph
* Wheel graph

## References

1. ↑ An Atlas of Graphs, p. 267-270
2. ↑ An Atlas of Graphs, p. 261

* 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

* Weisstein, Eric W.. "Archimedean Graph". http://mathworld.wolfram.com/ArchimedeanGraph.html.

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