I. Nasonov

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20242026

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math.MG2026

On $2 n + 4$ normals conjecture for convex polytopes in $R^{n}$

Ivan Nasonov, Gaiane Panina

We prove that for $n > 3$ each generic simple polytope in $R^{n}$ contains a point with at least $2 n + 4$ emanating normals to the boundary. This result is a piecewise-linear co…

math.MG2025

Each generic polytope in $R^{3}$ has a point with ten normals to the boundary

Ivan Nasonov, Gaiane Panina

It is conjectured since long that each smooth convex body $P \subset R^{n}$ has a point in its interior which belongs to at least $2 n$ normals from different points…

math.MG2024

Concurrent normals problem for convex polytopes and Euclidean distance degree

Ivan Nasonov, Gaiane Panina, Dirk Siersma

It is conjectured since long that for any convex body $P \subset R^{n}$ there exists a point in its interior which belongs to at least $2 n$ normals from different points on t…

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

Each generic polytope in R3 has a point with ten normals to the boundary

Concurrent normals problem for convex polytopes and Euclidean distance degree

On $2 n + 4$ normals conjecture for convex polytopes in $R^{n}$

Each generic polytope in $R^{3}$ has a point with ten normals to the boundary