The Tammes Problem for N = 14

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 (195...

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Bibliographic Details
Published in:Experimental mathematics 2015-10, Vol.24 (4), p.460-468
Main Authors: Musin, Oleg R., Tarasov, Alexey S.
Format: Article
Language:English
Subjects:
irreducible contact graph
sphere packing
Tammes problem
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Summary: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.
ISSN:1058-6458
1944-950X
DOI:10.1080/10586458.2015.1022842