The kissing number in four dimensions

Details The kissing number in four dimensions The kissing number in four dimensions

2003-09-26

arxiv.org/abs/math/0309430v3

Annals of Mathematics, 168 (2008), No. 1, 1-32

Mathematics

Metric Geometry

30 pages, 9 figures

Scientific paper

The kissing number problem asks for the maximal number k(n) of equal size nonoverlapping spheres in n-dimensional space that can touch another sphere of the same size. This problem in dimension three was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. In three dimensions the problem was finally solved only in 1953 by Sch\"utte and van der Waerden. In this paper we present a solution of a long-standing problem about the kissing number in four dimensions. Namely, the equality k(4)=24 is proved. The proof is based on a modification of Delsarte's method.

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