A method for generating star polytopes using group theory

Ying Wang; Liang Zhao

doi:10.1117/12.2686186

28 July 2023 A method for generating star polytopes using group theory

Ying Wang, Liang Zhao

Proceedings Volume 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023); 1275634 (2023) https://doi.org/10.1117/12.2686186
Event: 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), 2023, Tangshan, China

Abstract

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.

Citation Download Citation

Ying Wang and 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

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