Archimedean Graph


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 GconnectivityVE|Aut(G)|HamiltonianEulerianvertex-transitiveedge-transitive
cuboctahedral graphquartic122448yesyesyesyes
great rhombicosidodecahedral graphcubic120180120yesnoyesno
great rhombicuboctahedral graphcubic487248yesnoyesno
icosidodecahedral graphquartic3060120yesyesyesyes
small rhombicosidodecahedral graphquartic60120120yesyesyesno
small rhombicuboctahedral graphquartic244848yesyesyesno
snub cubical graphquintic246024yesnoyesno
snub dodecahedral graphquintic6015060yesnoyesno
truncated cubical graphcubic243648yesnoyesno
truncated dodecahedral graphcubic6090120yesnoyesno
truncated icosahedral graphcubic6090120yesnoyesno
truncated octahedral graphcubic243648yesnoyesno
truncated tetrahedral graphcubic121824yesnoyesno

See also

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

Explore with Wolfram|Alpha


Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, pp. 263 and 266, 1998.

Referenced on Wolfram|Alpha

Archimedean Graph

Cite this as:

Weisstein, Eric W. "Archimedean Graph." From MathWorld--A Wolfram Web Resource.

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