, Volume 27, Issue 3, pp 353-375
Date: 01 Jan 2002

Closed-Form Expressions for Uniform Polyhedra and Their Duals

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Abstract

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.

Received September 20, 2000, and in revised form September 20, 2001. Online publication February 19, 2002.