The complete set of uniform polyhedra

1975/03/06 by John Skilling · 5 citations
Computer Science · Mathematics · Engineering · #Advanced Graph Theory Research #Advanced Combinatorial Mathematics #graph theory and CDMA systems #Polyhedron #Combinatorics #Mathematics #Set (abstract data type) #Coxeter group #Computer science

paper · doi:10.1098/rsta.1975.0022

openalex publication_date 1975/03/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/05/21

Abstract

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.

Citations

• Uniform polyhedra

Cited by

• Uniform solution for uniform polyhedra
• Closed-Form Expressions for Uniform Polyhedra and Their Duals
• Isogonal Prismatoids
• List of uniform polyhedra [wikipedia]
• Uniform polyhedron [wikipedia]