Variations on five-dimensional sphere packings
Metric Geometry
2026-03-05 v3 Combinatorics
Abstract
We analyze Sz\"oll\H{o}si's recent construction of a conjecturally optimal five-dimensional kissing configuration and produce a new such configuration, the fourth to be discovered. We construct five-dimensional sphere packings from these configurations, which augment Conway and Sloane's list of conjecturally optimal packings. We also construct a new kissing configuration in nine dimensions. None of these constructions improves on the known records, but they provide geometrically distinct constructions achieving these records.
Keywords
Cite
@article{arxiv.2412.00937,
title = {Variations on five-dimensional sphere packings},
author = {Henry Cohn and Isaac Rajagopal},
journal= {arXiv preprint arXiv:2412.00937},
year = {2026}
}
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17 pages