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arXiv · 2301.13076

Extremal spherical polytopes and Borsuk's conjecture

Mikhail Katz·Facundo Mémoli·Qingsong Wang
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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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Mikhail Katz, Facundo Mémoli, Qingsong Wang. 2024-11-11. Extremal spherical polytopes and Borsuk's conjecture. https://arxiv.org/abs/2301.13076

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