A note on five dimensional kissing arrangements

Abstract

The kissing number τ (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 τ (5), and refutes a 'belief' of Cohn-Jiao-