On the packing of fourteen congruent spheres in a cube
The classical problem of finding the configuration of \(n\) points in a unit cube of the 3-dimensional Euclidean space for which the minimum mutual distance is maximal was determined by Schaer, for \(n\leq 10\). In [Math. Mag. 44, 199--208 (1971; Zbl 0228.52004)], \textit{M. Goldberg} has given up to \(n=27\) configurations suspected to be the optimal arrangements. In this paper, the author proves that the maximum of the minimum distance of \(14\) points in the 3-dimensional unit cube is \(\frac{\sqrt 2}{2}\), and at the same time Goldberg's conjecture is proved for \(n=14\).
scientific article; zbMATH DE number 5571620
scientific article