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Optimality and uniqueness of the $D_4$ root system

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arxiv 2404.18794 v2 pith:YJ3DNC6E submitted 2024-04-29 math.MG math.OC

David de Laat , Nando M. Leijenhorst , Willem H. H. de Muinck Keizer This is my paper · ORCID
classification math.MGmath.OC
keywords optimalkissingmathbbrootsystemboundcellcode
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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 $77$.

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Cited by 1 Pith paper

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  1. Variations on five-dimensional sphere packings

    math.MG 2024-12 accept novelty 7.0 of 10

    New non-isometric kissing configurations are constructed in dimensions 5 and 9, and the uniform 5D packings containing the known kissing configurations are classified.

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