Icosidodecahedral Graph


A quartic symmetric graph on 30 nodes and 60 edges corresponding to the skeleton of the Archimdean icosidodecahedron, great dodecahemidodecahedron, great icosidodecahedron, great icosihemidodecahedron, small dodecahemidodecahedron, and small icosihemidodecahedron. It is illustrated above in a number of symmetrical embeddings.


It has a total of 78080 distinct (directed) Hamiltonian cycles, which yield two inequivalent order-6 generalized LCF notations, one of order 3, two of order 2, and 649 of order 1. The LCF embeddings of order greater than one are illustrated above.

It has graph diameter 5, graph radius 5, and chromatic number 3. Its graph spectrum is (-2)^(10)(1-sqrt(5))^3(-1)^41^42^5(1+sqrt(5))^34^1.

It is the line graph of the dodecahedral graph.

See also

Icosidodecahedron, Quartic Symmetric Graph

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Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, p. 267, 1998.

Cite this as:

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

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