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arXiv · 2610.13475

Each simplex in $\mathbb{R}^4$ has a point with at least $14$ emanating normals to its boundary

Ivan Nasonov·Gaiane Panina
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Abstract

We prove that each simplex in $\mathbb{R}^4$ contains a point with at least $14$ emanating normals to the boundary. Earlier, the authors proved that each generic simple polytope in $\mathbb{R}^4$ contains a point with at least $12$ emanating normals to the boundary. This problem belongs to a piecewise linear counterpart of a longstanding problem concerning normals to smooth convex bodies.

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Ivan Nasonov, Gaiane Panina. 2026-10-09. Each simplex in $\mathbb{R}^4$ has a point with at least $14$ emanating normals to its boundary. https://arxiv.org/abs/2610.13475

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