English

Extremal spherical polytopes and Borsuk's conjecture

Combinatorics 2024-11-12 v3 Metric Geometry

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.

Keywords

Cite

@article{arxiv.2301.13076,
  title  = {Extremal spherical polytopes and Borsuk's conjecture},
  author = {Mikhail Katz and Facundo Mémoli and Qingsong Wang},
  journal= {arXiv preprint arXiv:2301.13076},
  year   = {2024}
}

Comments

Content disagreement among the authors

R2 v1 2026-06-28T08:27:08.346Z