  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.
