August 17, 2025

Algorithms for classifying regular polytopes with a fixed automorphism group

Key Points

Improved algorithms classify regular polytopes for fixed automorphism groups, enhancing computational efficiency.
The original algorithm's computational times and memory requirements were thoroughly analyzed to assess performance.
An innovative isomorphism testing algorithm was proposed, aimed at optimizing comparisons among polytopes.
Results indicate successful classification of regular polytopes in relation to certain alternating groups and the sporadic group Co3.

Abstract

In this paper, various algorithms used in the classifications of regular polytopes for given groups are compared. First computational times and memory usages are analyzed for the original algorithm used in one of these classifications. Second, a possible algorithm for isomorphism testing among polytopes is suggested. Then, two improved algorithms are compared, and finally, results are given for a new classification of all regular polytopes for certain alternating groups and for the sporadic group Co3.

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