Extremal spherical polytopes and Borsuk's conjecture

2023/01/30 by Mikhail G. Katz, Katz, Mikhail, Facundo Mémoli +3
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2301.13076

openalex publication_date 2023/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generate anti-self-polar polytopes via a numerical implementation of the gradient flow induced by the diameter functional on the space of all finite subsets of the sphere, and prove related results on the critical points of the diameter functional as well as results about the combinatorics of such polytopes. We also discuss potential connections to Borsuk's conjecture.

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