Snub Cubical Graph


The snub cubical graph is the Archimedean graph on 24 nodes and 60 edges obtained by taking the skeleton of the snub cube. It is a quintic graph, is planar, Hamiltonian, and has chromatic number 3. Several embeddings are illustrated above.

It is implemented in the Wolfram Language as GraphData["SnubCubicalGraph"].

It is vertex-transitive, although not edge-transitive because some edges are part of three-circuits while others are not.


The snub cubical graph has 1690680 distinct (directed) Hamiltonian cycles, giving two LCF-type notations of order 4 (illustrated above), 12 of order 3 (illustrated above), 627 of order 2, and 70127 of order 1.

Its graph spectrum is given by (-1-sqrt(3))^2x^3(1-sqrt(7))^3(-1)^4y^3(-1+sqrt(3))^2z^3(1+sqrt(7))^35^1, where x, y, and z are the roots of x^3+x^2-4x-2. Its automorphism group is of order |Aut(G)|=24.

See also

Archimedean Graph, Quintic Graph, Snub Cube, Snub Dodecahedral Graph

Explore with Wolfram|Alpha


Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, p. 268, 1998.

Cite this as:

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

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