Sphere packings IV
Abstract
This is the sixth in a series of papers giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than $\pi/\sqrt{18}\approx 0.74048...$. This is the oldest problem in discrete geometry and is an important part of Hilbert's 18th problem. An example of a packing achieving this density is the face-centered cubic packing. This paper completes part of the fourth step of the program outlined in math.MG/9811073: A proof that if some standard region has more than four sides, then the star scores less than $8 \pt$.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- November 1998
- DOI:
- 10.48550/arXiv.math/9811076
- arXiv:
- arXiv:math/9811076
- Bibcode:
- 1998math.....11076H
- Keywords:
-
- Metric Geometry
- E-Print:
- 53 pages. Sixth in a series beginning with math.MG/9811071