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Platonic graph : ウィキペディア英語版 | 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.〔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.〕 * 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 == See also==
*Regular map (graph theory) *Archimedean graph *Wheel graph
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