Sphere packings, II

Sphere packings, II

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Article ID: iaor19981403
Country: United States
Volume: 18
Issue: 2
Start Page Number: 135
End Page Number: 149
Publication Date: Sep 1997
Journal: Discrete and Computational Geometry
Authors:
Keywords: location
Abstract:

An earlier paper describes a program to prove the Kepler conjecture on sphere packings. This paper carries out the second step of that program. A sphere packing leads to a decomposition of ℝ3 into polyhedra. The polyhedra are divided into two classes. The first class of polyhedra, called quasi-regular tetrahedra, have density at most that of a regular tetrahedron. The polyhedra in the remaining class have density at most that of a regular octahedron (about 0.7209).

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