Sphere packings revisited

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Abstract

In this paper we survey most of the recent and often surprising results on packings of congruent spheres in d-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, the strong dodecahedral conjecture and the truncated octahedral conjecture;-the strong Kepler conjecture;-bounds on the density of sphere packings in higher dimensions;-solidity and uniform stability. Each topic is discussed in details along with some of the "most wanted" research problems. © 2005 Elsevier Ltd. All rights reserved.

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Bezdek, K. (2006). Sphere packings revisited. European Journal of Combinatorics, 27(6), 864–883. https://doi.org/10.1016/j.ejc.2005.05.001

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