The Tammes problem for N=14
Metric Geometry
2015-09-09 v2 Combinatorics
Abstract
The Tammes problem is to find the arrangement of N points on a unit sphere which maximizes the minimum distance between any two points. This problem is presently solved for several values of N, namely for N=3,4,6,12 by L. Fejes Toth (1943); for N=5,7,8,9 by Schutte and van der Waerden (1951); for N=10,11 by Danzer (1963) and for N=24 by Robinson (1961). Recently, we solved the Tammes problem for N=13. The optimal configuration of 14 points was conjectured more than 60 years ago. In the paper, we give a solution of this long-standing open problem in geometry. Our computer-assisted proof relies on an enumeration of the irreducible contact graphs.
Cite
@article{arxiv.1410.2536,
title = {The Tammes problem for N=14},
author = {Oleg R. Musin and Alexey S. Tarasov},
journal= {arXiv preprint arXiv:1410.2536},
year = {2015}
}
Comments
14 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1002.1439