Chapter 10
The Stellated Icosahedra

Overview

The enumeration of all stellations of the icosahedron was accomplished in 1938. The geometric constructions and combinatorial algorithms used can easily be programmed in Mathematica. Its symbolic and graphic capabilities make it well suited to render the solids in a variety of formats.

Section 1 introduces stellations of regular polyhedra and discusses stellations of the octahedron and dodecahedron. Section 2 shows how all stellations of the icosahedron can be generated and represented as symbolic objects in Mathematica. In Section 3 we turn to the numerical aspects and generate three-dimensional graphic objects for the stellations. At the end, we discuss some of the interesting stellations.

Programs

Icosahedra.m

Notebooks

Icosahedra.nb

Color Plates

Plate 2

Plate 6

Resources on the Internet

The Stellated Icosahedra

Images of all 59 stellated icosahedra and part of the text from this chapter.