Archimedean Graph

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ArchimedeanGraph

A graph corresponding to the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, all of which are regular, planar, polyhedral, and Hamiltonian.

The following table lists the Archimedean graphs G, their connectivity d, number of vertices V, number of edges E, order of the automorphism group, Hamiltonicity, Eulerianicity, vertex-transitivity, and edge-transitivity. Note that all Archimedean graphs are Hamiltonian, vertex-transitive.

graph G connectivity V E |Aut(G)| Hamiltonian Eulerian vertex-transitive edge-transitive

cuboctahedral graph quartic 12 24 48 yes yes yes yes

great rhombicosidodecahedral graph cubic 120 180 120 yes no yes no

great rhombicuboctahedral graph cubic 48 72 48 yes no yes no

icosidodecahedral graph quartic 30 60 120 yes yes yes yes

small rhombicosidodecahedral graph quartic 60 120 120 yes yes yes no

small rhombicuboctahedral graph quartic 24 48 48 yes yes yes no

snub cubical graph quintic 24 60 24 yes no yes no

snub dodecahedral graph quintic 60 150 60 yes no yes no

truncated cubical graph cubic 24 36 48 yes no yes no

truncated dodecahedral graph cubic 60 90 120 yes no yes no

truncated icosahedral graph cubic 60 90 120 yes no yes no

truncated octahedral graph cubic 24 36 48 yes no yes no

truncated tetrahedral graph cubic 12 18 24 yes no yes no

See also

Archimedean Dual Graph, Archimedean Solid, Cubic Graph, Platonic Graph, Quartic Graph, Quintic Graph, Regular Graph

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References

House of Graphs. Archimedean Graphs. Cuboctahedral Graph, Great Rhombicosidodecahedral Graph, Great Rhombicuboctahedral Graph, Icosidodecahedral Graph, Small Rhombicosidodecahedral Graph, Small Rhombicuboctahedral Graph, Snub Cubical Graph, Snub Dodecahedral Graph, Truncated Cubical Graph, Truncated Dodecahedral Graph, Truncated Icosahedral Graph, Truncated Octahedral Graph, and Truncated Tetrahedral Graph.Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, pp. 263 and 266, 1998.

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Archimedean Graph

Cite this as:

Weisstein, Eric W. "Archimedean Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ArchimedeanGraph.html

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