78 citations · 310 across the 39 of their papers we have counts for
8 papers · 2 filters
Sphere packings II
Thomas C. Hales
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 decompos…
Sphere packings I
Thomas C. Hales
We describe a program to prove the Kepler conjecture on sphere packings. We then carry out the first step of this program. Each packing determines a decomposition of space into Del…
A proof of the dodecahedral conjecture
Thomas C. Hales, Sean McLaughlin
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 inradiu…
The Kepler conjecture
Thomas C. Hales
This is the eighth and final paper in a series giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is neve…
Sphere packings IV
Thomas C. Hales
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 great…
Sphere packings III
Thomas C. Hales
This is the fifth 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 great…