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arXiv · 2512.15511

Symmetric polytopes whose automorphism groups are 2-groups

Gabriel Cunningham·Yan-Quan Feng·Dong-Dong Hou·Egon Schulte
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Abstract

The present work investigates regular, semiregular, and chiral polytopes of any rank $d\geq 3$, whose automorphism groups are 2-groups. There is a large variety of rather small finite regular or alternating semiregular polytopes with automorphism groups of 2-power order: for such polytopes with toroidal sections of rank 3, the various sections of rank 3 can be entirely prescribed (possibly with one exception in the semiregular case). It is also shown that having a 2-group as automorphism group is hereditary under taking universal extensions: the universal extension of a given regular, chiral, or alternating semiregular polytope with a finite or infinite 2-group as automorphism group, is a polytope of one rank higher with an infinite 2-group an automorphism group.

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Gabriel Cunningham, Yan-Quan Feng, Dong-Dong Hou, Egon Schulte. 2025-12-17. Symmetric polytopes whose automorphism groups are 2-groups. https://arxiv.org/abs/2512.15511

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