Sphere packings V

Details Sphere packings V Sphere packings V

1998-11-11

arxiv.org/abs/math/9811077v1

Mathematics

Metric Geometry

54 pages. Seventh in a series beginning with math.MG/9811071. The author's home page is http://www.math.lsa.umich.edu/~samf/

Scientific paper

The Hales program to prove the Kepler conjecture on sphere packings consists of five steps, which if completed, will jointly comprise a proof of the conjecture. We carry out step five of the program [outlined in math.MG/9811073], a proof that the local density of a certain combinatorial arrangement, the pentahedral prism, is less than that of the face-centered cubic lattice packing. We prove various relations on the local density using computer-based interval arithmetic methods. Together, these relations imply the local density bound.

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