close packing

Define the packing density η of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for identical spheres: cubic lattice, face-centered cubic lattice, and hexagonal lattice. It was hypothesized by Kepler in 1611 that close packing (cubic or hexagonal, which have equivalent packing densities) is the densest possible, and this assertion is known as the Kepler conjecture. The problem of finding the densest packing of spheres (not necessarily periodic) is therefore known as the Kepler problem, where η_Kepler = η_(F C C) = η_(H C P) = π/(3sqrt(2))≈74.048% (OEIS A093825; Steinhaus 1999, p. 202; Wells 1986, p. 29; Wells 1991, p. 237).

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