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 facecentered 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 eprints
 Pub Date:
 November 1998
 DOI:
 10.48550/arXiv.math/9811076
 arXiv:
 arXiv:math/9811076
 Bibcode:
 1998math.....11076H
 Keywords:

 Metric Geometry
 EPrint:
 53 pages. Sixth in a series beginning with math.MG/9811071