Mathematical Research Letters

Volume 30 (2023)

Number 5

A note on five dimensional kissing arrangements

Pages: 1609 – 1615

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n5.a13

Author

Ferenc Szöllősi (Department of Mathematical Sciences, Interdisciplinary Faculty of Science and Engineering, Shimane University, Matsue, Japan)

Abstract

The kissing number $\tau (d)$ is the maximum number of pairwise non-overlapping unit spheres each touching a central unit sphere in the $d$-dimensional Euclidean space. In this note we report on how we discovered a new, previously unknown arrangement of 40 unit spheres in dimension $5$. Our arrangement saturates the best known lower bound on $\tau (5)$, and refutes a ‘belief’ of Cohn–Jiao–Kumar–Torquato.

Received 19 January 2023

Accepted 20 February 2023

Published 14 May 2024