Stability of the simplex bound for packings by equal spherical caps determined by simplicial regular polytopes
K\'aroly B\"or\"oczky, K\'aroly J. B\"or\"oczky, Alexey Glazyrin and, \'Agnes Kov\'acs
TL;DR
This paper proves a stability version of the known optimal packing of equal spherical caps determined by vertices of Euclidean simplicial regular polytopes, showing the robustness of this packing configuration.
Contribution
It introduces a stability result for the optimal packing of equal spherical caps by vertices of simplicial regular polytopes, extending the classical optimality result.
Findings
Stability of the simplex bound for spherical packings
Robustness of optimal packings under perturbations
Extension of classical packing results
Abstract
It is well known that the vertices of any Euclidean simplicial regular polytope determine an optimal packing of equal spherical balls. We prove a stability version of optimal order of this result.
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