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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.09434 |
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| _version_ | 1866910448524197888 |
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| author | Montero, Antonio Toledo, Micael |
| author_facet | Montero, Antonio Toledo, Micael |
| contents | Abstract polytopes are combinatorial objects that generalise geometric objects such as convex polytopes, maps on surfaces and tilings of the space. Chiral polytopes are those abstract polytopes that admit full combinatorial rotational symmetry but do not admit reflections. In this paper we build chiral polytopes whose facets (maximal faces) are isomorphic to a prescribed regular cubic tessellation of the $n$-dimensional torus ($n \geq 2$). As a consequence, we prove that for every $d \geq 3$ there exist infinitely many chiral $d$-polytopes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09434 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chiral extensions of regular toroids Montero, Antonio Toledo, Micael Combinatorics 52B15, 52C22, 05E18 Abstract polytopes are combinatorial objects that generalise geometric objects such as convex polytopes, maps on surfaces and tilings of the space. Chiral polytopes are those abstract polytopes that admit full combinatorial rotational symmetry but do not admit reflections. In this paper we build chiral polytopes whose facets (maximal faces) are isomorphic to a prescribed regular cubic tessellation of the $n$-dimensional torus ($n \geq 2$). As a consequence, we prove that for every $d \geq 3$ there exist infinitely many chiral $d$-polytopes. |
| title | Chiral extensions of regular toroids |
| topic | Combinatorics 52B15, 52C22, 05E18 |
| url | https://arxiv.org/abs/2405.09434 |