The strong thirteen spheres problem
The authors present a computer-assisted proof of the long-standing open Tammes problem for 13 points, asking, in general, for the distribution of \(N\) points on the sphere such that the minimal angular distance among them is maximized. The optimal arrangement, which is also proved to be unique up to isometry, can already be found in [\textit{L. Fejes Tóth}, Lagerungen in der Ebene, auf der Kugel und im Raum. Berlin-Göttingen-Heidelberg: Springer-Verlag (1953; Zbl 0052.18401)]. Due to its close relation to the famous and classical 3-dimensional kissing number problem, the Tammes problem for 13 spheres is also called the ``strong thirteen spheres problem''.
scientific article; zbMATH DE number 6065213
scientific article