Platonic graph

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The platonic graphs can be seen as Schlegel diagrams of the platonic solids. (excluding the square pyramid also shown here)

In the mathematical field of graph theory, a Platonic graph is a graph that has one of the Platonic solids as its skeleton. There are 5 Platonic graphs, and all of them are regular, polyhedral (and therefore by necessity also 3-vertex-connected, vertex-transitive, edge-transitive and planar graphs), and also Hamiltonian graphs.[1]

Orthogonal projections of platonic solids

See also

References

  1. ^ Read, R. C. and Wilson, R. J. An Atlas of Graphs, Oxford, England: Oxford University Press, 2004 reprint, Chapter 6 special graphs pp. 261, 266.

External links

  • Weisstein, Eric W. "Platonic graph". MathWorld.
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