The one-sided kissing number in four dimensions
Metric Geometry
2007-05-23 v5 Combinatorics
Abstract
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.
Cite
@article{arxiv.math/0511071,
title = {The one-sided kissing number in four dimensions},
author = {Oleg R. Musin},
journal= {arXiv preprint arXiv:math/0511071},
year = {2007}
}