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.)

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