Generating and Rendering Four-Dimensional Polytopes

Volume 1, Issue 3
Winter 1991

The regular polytopes in four dimensions can be generated easily by the judicious use of their symmetry groups, and can be rendered in three dimensions in stereographic projection. In this article we construct one such polytope, introducing the relevant group-theory concepts as needed. The result can be viewed with Mathematica graphics, or with a more sophisticated renderer such as RenderMan.