Finite point-sets on S2 with minimum distance as large as possible
Discrete Mathematics
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Erdős distance problems in normed spaces
Computational Geometry: Theory and Applications
On the maximum number of touching pairs in a finite packing of translates of a convex body
Journal of Combinatorial Theory Series A
The Thirteen Spheres: A New Proof
Discrete & Computational Geometry
Packing unit spheres into the smallest sphere using VNS and NLP
Computers and Operations Research
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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.