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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Received April 24, 1995, and in revised form April 11, 1996.
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Hales, T. Sphere Packings, II . Discrete Comput Geom 18, 135–149 (1997). https://doi.org/10.1007/PL00009312
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DOI: https://doi.org/10.1007/PL00009312
Keywords
- Early Paper
- Sphere Packing
- Regular Tetrahedron
- Regular Octahedron
- Kepler Conjecture