The Stellated Icosahedra

by Roman E. Maeder

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.

This document is an excerpt of an article published in Mathematica in Education [Maeder94b]. An expanded version appears in Chapter 10 of R. Maeder's book The Mathematica Programmer II.


Copyright by Roman E. Maeder, 1995

Introduction

Stellations of the Icosahedron

Enumeration of all Possibilities

Rendering

Discussion of the Solids

All 59 Pictures


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