The one-sided kissing number in four dimensions

Details The one-sided kissing number in four dimensions The one-sided kissing number in four dimensions

2005-11-03

arxiv.org/abs/math/0511071v5

Periodica Math. Hungarica, vol. 53, No. 1-2 (September 2006), pp. 209-225

Mathematics

Metric Geometry

Scientific paper

Let H be a closed half-space of n-dimensional Euclidean space. Suppose S is a unit sphere in H that touches the supporting hyperplane of H. The one-sided kissing number B(n) is the maximal number of unit nonoverlapping spheres in H that can touch S. Clearly, B(2)=4. It was proved that B(3)=9. Recently, K. Bezdek proved that B(4)=18 or 19, and conjectured that B(4)=18. We present a proof of this conjecture.

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