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Sphere Packings, II
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  • Published: September 1997

Sphere Packings, II

  • T. C. Hales1 

Discrete & Computational Geometry volume 18, pages 135–149 (1997)Cite this article

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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 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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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA, , , , , , US

    T. C. Hales

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  1. T. C. Hales
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Received April 24, 1995, and in revised form April 11, 1996.

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Cite this article

Hales, T. Sphere Packings, II . Discrete Comput Geom 18, 135–149 (1997). https://doi.org/10.1007/PL00009312

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  • Issue Date: September 1997

  • DOI: https://doi.org/10.1007/PL00009312

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Keywords

  • Early Paper
  • Sphere Packing
  • Regular Tetrahedron
  • Regular Octahedron
  • Kepler Conjecture
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