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The Complete Set of Uniform Polyhedra

J. Skilling
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 278, No. 1278 (Mar. 6, 1975), pp. 111-135
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/74475
Page Count: 26
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The Complete Set of Uniform Polyhedra
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Abstract

A definitive enumeration of all uniform polyhedra is presented (a uniform polyhedron has all vertices equivalent and all its faces regular polygons). It is shown that the set of uniform polyhedra presented by Coxeter, Longuet-Higgins & Miller (1953) is essentially complete. However, after a natural extension of their definition of a polyhedron to allow the coincidence of two or more edges, one extra polyhedron is found, namely the great disnub dirhombidodecahedron.

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