Article ID: | iaor19981403 |
Country: | United States |
Volume: | 18 |
Issue: | 2 |
Start Page Number: | 135 |
End Page Number: | 149 |
Publication Date: | Sep 1997 |
Journal: | Discrete and Computational Geometry |
Authors: | Hales T.C. |
Keywords: | location |
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 ℝ3 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).