Discrete & Computational Geometry

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

Sphere Packings, II

  • T. C. Hales


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).


Early Paper Sphere Packing Regular Tetrahedron Regular Octahedron Kepler Conjecture 
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Copyright information

© Springer-Verlag New York Inc. 1997

Authors and Affiliations

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

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