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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.
Ying Wang andLiang Zhao
"A method for generating star polytopes using group theory", Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 1275634 (28 July 2023); https://doi.org/10.1117/12.2686186
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Ying Wang, Liang Zhao, "A method for generating star polytopes using group theory," Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 1275634 (28 July 2023); https://doi.org/10.1117/12.2686186