The Mathematica Programmer

Uniform Polyhedra

Volume 3, Issue 4
Fall 1993

Uniform polyhedra consist of regular faces and congruent vertices. Allowing for non-convex faces and vertex figures, there are 75 such polyhedra, as well as two infinite families of prisms and antiprisms. A recently discovered uniform way of computing their vertex coordinates is the basis for our program to display all of these solids, among which are many beautiful and stunning shapes. We will also develop some utilities for drawing spherical triangles and for storing properties of objects in a flexible way.