A method for generating star polytopes using group theory
Ying Wang, Liang Zhao · 2023
This paper presents a method for generating 3D and 4D star polytopes based on the Todd-Coxeter algorithm and Wythoff construction. This method can be used to calculate most of the 3-dimensional uniform star polytopes and all of the 4-dimensional uniform star polytopes. Its advantage is that it can obtain the group element representation corresponding to each vertex, edge, and face of the polytope without using floating-point arithmetic, where each group element is given by the product of the generators. With slight modifications, it can also be applied to calculate all convex Wythoff uniform polytopes.