Constructing new geometries: a generalized approach to halving for hypertopes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909212752216064 |
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| author | Piedade, Claudio Alexandre Tranchida, Philippe |
| author_facet | Piedade, Claudio Alexandre Tranchida, Philippe |
| contents | Given a residually connected incidence geometry $Γ$ that satisfies two conditions, denoted $(B_1)$ and $(B_2)$, we construct a new geometry $H(Γ)$ with properties similar to those of $Γ$. This new geometry $H(Γ)$ is inspired by a construction of Percsy, Percsy and Leemans [1]. We show how $H(Γ)$ relates to the classical halving operation on polytopes, allowing us to generalize the halving operation to a broader class of geometries, that we call non-degenerate leaf hypertopes. Finally, we apply this generalization to cubic toroids in order to generate new examples of regular hypertopes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19050 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constructing new geometries: a generalized approach to halving for hypertopes Piedade, Claudio Alexandre Tranchida, Philippe Combinatorics Group Theory 52B11, 51E24, 05E18, 05B25, 20D99 Given a residually connected incidence geometry $Γ$ that satisfies two conditions, denoted $(B_1)$ and $(B_2)$, we construct a new geometry $H(Γ)$ with properties similar to those of $Γ$. This new geometry $H(Γ)$ is inspired by a construction of Percsy, Percsy and Leemans [1]. We show how $H(Γ)$ relates to the classical halving operation on polytopes, allowing us to generalize the halving operation to a broader class of geometries, that we call non-degenerate leaf hypertopes. Finally, we apply this generalization to cubic toroids in order to generate new examples of regular hypertopes. |
| title | Constructing new geometries: a generalized approach to halving for hypertopes |
| topic | Combinatorics Group Theory 52B11, 51E24, 05E18, 05B25, 20D99 |
| url | https://arxiv.org/abs/2405.19050 |