Discrete & Computational Geometry

, Volume 27, Issue 3, pp 353-375

First online:

Closed-Form Expressions for Uniform Polyhedra and Their Duals

  • Peter W.  MesserAffiliated with4315 West Riverlake Drive, Mequon, WI 53092-4856, USA

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A uniform polyhedron has equivalent vertices and regular polygonal faces. An established set of 77 Wythoff symbols effectively describes the dynamic kaleidoscopic constructions of uniform polyhedra. The main combinatorial and metrical quantities of uniform polyhedra and their duals are presented as closed-form expressions derived from the Wythoff symbols.