On $2n+4$ normals conjecture for convex polytopes in $\mathbb{R}^n$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866912816576856064 |
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| author | Nasonov, Ivan Panina, Gaiane |
| author_facet | Nasonov, Ivan Panina, Gaiane |
| contents | We prove that for $n>3$ each generic simple polytope in $\mathbb{R}^n$ contains a point with at least $2n+4$ emanating normals to the boundary.
This result is a piecewise-linear counterpart of a long-standing problem about normals to smooth convex bodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22695 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On $2n+4$ normals conjecture for convex polytopes in $\mathbb{R}^n$ Nasonov, Ivan Panina, Gaiane Metric Geometry Geometric Topology We prove that for $n>3$ each generic simple polytope in $\mathbb{R}^n$ contains a point with at least $2n+4$ emanating normals to the boundary. This result is a piecewise-linear counterpart of a long-standing problem about normals to smooth convex bodies. |
| title | On $2n+4$ normals conjecture for convex polytopes in $\mathbb{R}^n$ |
| topic | Metric Geometry Geometric Topology |
| url | https://arxiv.org/abs/2510.22695 |