Discrete & Computational Geometry

, Volume 18, Issue 2, pp 135–149 | Cite as

Sphere Packings, II

  • T. C. Hales

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).

Keywords

Early Paper Sphere Packing Regular Tetrahedron Regular Octahedron Kepler Conjecture 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© 1997 Springer-Verlag New York Inc.

Authors and Affiliations

  • T. C. Hales
    • 1
  1. 1.Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USAUS

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