Sphere packings revisited

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:– er numbers of convex bodies and kissing numbers of spheres; ng numbers of convex bodies; numbers of convex bodies; ded Hadwiger and kissing numbers; t graphs of finite packings and the combinatorial Kepler problem; imetric problems for Voronoi cells, the strong dodecahedral conjecture and the truncated octahedral conjecture; rong Kepler conjecture; on the density of sphere packings in higher dimensions; ty and uniform stability. opic is discussed in details along with some of the “most wanted” research problems.