Generating and Rendering Four-Dimensional Polytopes

by John M. Sullivan

Published in The Mathematica Journal, 1:3, 1991, pp 76-85. Plain-English Abstract

This expository paper shows a nice way to generate coordinates for the regular polytopes in three and four dimensions, and describes how to picture the four-dimensional polytopes via stereographic projection as bubble clusters in three-space. It is illustrated with computer graphics using a custom bubble shader for Renderman.