A note on five dimensional kissing arrangements

TL;DR

This paper reports the discovery of a new 40-sphere arrangement in five dimensions that matches the best known lower bound for the kissing number, challenging previous beliefs about such configurations.

Contribution

It introduces a previously unknown five-dimensional sphere arrangement that saturates the known lower bound for the kissing number, providing new insights into high-dimensional packing.

Findings

Discovered a 40-sphere arrangement in 5D space

Refutes previous beliefs about kissing number configurations

Matches the best known lower bound for $ au(5)$

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.