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.
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