A proof of the dodecahedral conjecture

Abstract

The dodecahedral conjecture states that the volume of the Voronoi polyhedron of a sphere in a packing of equal spheres is at least the volume of a regular dodecahedron with inradius 1. The authors prove the conjecture following the methodology of the proof the Kepler conjecture. (See math.MG/9811071.)

arXiv comment49 pages. The text has been completely rewritten in this version. The mathematical argument is the same as that presented in earlier versions

References in corpus (1)

• The Kepler conjecture

Cited by in corpus (4)

• An overview of the Kepler conjecture
• The geometric stability of Voronoi diagrams with respect to small changes of the sites
• Sphere Packings in 3 Dimensions
• On the 1-density of Unit Ball Covering