On ADEG-polyhedra in hyperbolic spaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918085354586112 |
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| author | Bredon, Naomi |
| author_facet | Bredon, Naomi |
| contents | In this paper, we establish that the non-zero dihedral angles of hyperbolic Coxeter polyhedra of large dimensions are not arbitrarily small. Namely, for dimensions $n\geq 32$, they are of the form $\fracπ{m}$ with $m\leq 6$. Moreover, this property holds in all dimensions $n\geq 7$ for Coxeter polyhedra with mutually intersecting facets. Then, we develop a constructive procedure tailored to Coxeter polyhedra with prescribed dihedral angles, from which we derive the complete classification of ADEG-polyhedra, characterized by having no pair of disjoint facets and dihedral angles $\fracπ{2}, \fracπ{3}$ and $\fracπ{6}$, only. Besides some well-known simplices and pyramids, there are three exceptional polyhedra, one of which is a new polyhedron $P_{\star}\subset \mathbb H^9$ with $14$ facets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On ADEG-polyhedra in hyperbolic spaces Bredon, Naomi Combinatorics Geometric Topology 20F55, 51M20 (primary), 52B11, 11R06 (secondary) In this paper, we establish that the non-zero dihedral angles of hyperbolic Coxeter polyhedra of large dimensions are not arbitrarily small. Namely, for dimensions $n\geq 32$, they are of the form $\fracπ{m}$ with $m\leq 6$. Moreover, this property holds in all dimensions $n\geq 7$ for Coxeter polyhedra with mutually intersecting facets. Then, we develop a constructive procedure tailored to Coxeter polyhedra with prescribed dihedral angles, from which we derive the complete classification of ADEG-polyhedra, characterized by having no pair of disjoint facets and dihedral angles $\fracπ{2}, \fracπ{3}$ and $\fracπ{6}$, only. Besides some well-known simplices and pyramids, there are three exceptional polyhedra, one of which is a new polyhedron $P_{\star}\subset \mathbb H^9$ with $14$ facets. |
| title | On ADEG-polyhedra in hyperbolic spaces |
| topic | Combinatorics Geometric Topology 20F55, 51M20 (primary), 52B11, 11R06 (secondary) |
| url | https://arxiv.org/abs/2507.05153 |