Sphere packings II

Details Sphere packings II Sphere packings II

1998-11-11

arxiv.org/abs/math/9811074v1

Discrete Comput. Geom. 18 (1997), 135-149

Mathematics

Metric Geometry

18 pages. Second of two older papers in the series on the proof of the Kepler conjecture. See math.MG/9811071. The original ab

Scientific paper

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 $R^3$ 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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