New non-isometric kissing configurations are constructed in dimensions 5 and 9, and the uniform 5D packings containing the known kissing configurations are classified.
A note on five dimensional kissing arrangements
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
citation-role summary
background 1
citation-polarity summary
fields
math.MG 1years
2024 1verdicts
ACCEPT 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Variations on five-dimensional sphere packings
New non-isometric kissing configurations are constructed in dimensions 5 and 9, and the uniform 5D packings containing the known kissing configurations are classified.