Sphere packings V

Samuel P. Ferguson

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arXiv · math/9811077

Sphere packings V

Samuel P. Ferguson

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Abstract

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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Samuel P. Ferguson. 1998-11-11. Sphere packings V. https://arxiv.org/abs/math/9811077

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