On 2n+4 normals conjecture for convex polytopes in ℝⁿ

2025/10/26 by Nasonov, Ivan, Panina, Gaiane
#FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2510.22695

Abstract

We prove that for n>3 each generic simple polytope in ℝⁿ 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.

Citations

• Concurrent normals problem for convex polytopes and Euclidean distance degree

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