Year: 2024
Type: preprint
Abstract: We prove that the $D_4$ root system (the set of vertices of the regular $24$-cell) is the unique optimal kissing configuration in $\mathbb R^4$, and is an optimal spherical code. For this, we use semidefinite programming to compute an exact optimal solution to the second level of the Lasserre hierarchy. We also improve the upper bound for the kissing number problem in $\mathbb R^6$ to $77$.
Source: arXiv (Cornell University)
Authors: de Laat, David, Leijenhorst, Nando M., Keizer, Willem H. H. de Muinck
Institution: Delft University of Technology
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4396821169