Platonic graph

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]

  • Tetrahedral graph – 4 vertices, 6 edges
  • Octahedral graph – 6 vertices, 12 edges
  • Cubical graph – 8 vertices, 12 edges
  • Icosahedral graph – 12 vertices, 30 edges
  • Dodecahedral graph – 20 vertices, 30 edges
Orthogonal projections of platonic solids
The platonic graphs can be seen as Schlegel diagrams of the platonic solids. (excluding the square pyramid also shown here)

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