Sphere packings in 3-space
نویسنده
چکیده
In this paper we survey results on packings of congruent spheres in 3-dimensional spaces of constant curvature. The topics discussed are as follows: Hadwiger numbers of convex bodies and kissing numbers of spheres; Touching numbers of convex bodies; Newton numbers of convex bodies; One-sided Hadwiger and kissing numbers; Contact graphs of finite packings and the combinatorial Kepler problem; Isoperimetric problems for Voronoi cells and the strong dodecahedral conjecture; The strong Kepler conjecture. Each topic is discussed in details along with some open problems. Four topics from the above list are treated in spaces of dimension different from three as well.
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