The complete set of uniform polyhedra

  title={The complete set of uniform polyhedra},
  author={James Skilling},
  journal={Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences},
  pages={111 - 135}
  • J. Skilling
  • Published 6 March 1975
  • Mathematics
  • Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
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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Uniform compounds of uniform polyhedra
  • J. Skilling
  • Art
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1976
Abstract The work of Coxeter, Longuet-Higgins and Miller (1953) and of Skilling (1975) is extended to give a complete list of uniform compounds of uniform polyhedra. Symmetry relationships between
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