The one-sided kissing number in four dimensions

نویسنده

Oleg R. Musin

چکیده

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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