The Tammes Problem for N = 14

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 Tóth (1943); for N = 5, 7, 8, 9 by Schütte 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 this article, we give a solution for this long-standing open problem in geometry. Our computer-assisted proof relies on an enumeration of the irreducible contact graphs.

2000 AMS Subject Classification::

• 52C17
• 05B40

Keywords:

• Tammes problem
• sphere packing
• irreducible contact graph

Notes

¹The authors of this program are Gunnar Brinkmann and Brendan McKay.