Optimality and uniqueness of the $D_4$ root system

David de Laat, Nando M. Leijenhorst, Willem H. H. de Muinck Keizer

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. F…