Symmetric polytopes whose automorphism groups are 2-groups
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914205626531840 |
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| author | Cunningham, Gabriel Feng, Yan-Quan Hou, Dong-Dong Schulte, Egon |
| author_facet | Cunningham, Gabriel Feng, Yan-Quan Hou, Dong-Dong Schulte, Egon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15511 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetric polytopes whose automorphism groups are 2-groups Cunningham, Gabriel Feng, Yan-Quan Hou, Dong-Dong Schulte, Egon Group Theory 20B25, 52B15, 51M20 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. |
| title | Symmetric polytopes whose automorphism groups are 2-groups |
| topic | Group Theory 20B25, 52B15, 51M20 |
| url | https://arxiv.org/abs/2512.15511 |