78 citations · 310 across the 39 of their papers we have counts for
21 papers · 1 filter
The Truncated Octahedral Conjecture
Thomas Hales, Lark Song
Among three-dimensional parallelohedra of fixed volume, the Archimedean truncated octahedron uniquely minimizes surface area, affirming a conjecture of K. Bezdek from 2006. The fin…
The Formal Proof of the Kepler Conjecture: a critical retrospective
Thomas Hales
The Kepler conjecture asserts that no packing of congruent balls in three-dimensional Euclidean space has density greater than that of the face-centered cubic packing. In 1998, Sam…
Packings of Regular Pentagons in the Plane
Thomas Hales, Wöden Kusner
We show that every packing of congruent regular pentagons in the Euclidean plane has density at most , which is about 0.92. More specifically, this article proves the…
A formal proof of the Kepler conjecture
Thomas Hales, Mark Adams, Gertrud Bauer +19
This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the…
A Proof of Fejes Toth's Conjecture on Sphere Packings with Kissing Number Twelve
Thomas C. Hales
In 1969, Fejes Toth conjectured that in Euclidean 3-space any packing of equal balls such that each ball is touched by twelve others consists of hexagonal layers. This article veri…
The Strong Dodecahedral Conjecture and Fejes Toth's Conjecture on Sphere Packings with Kissing Number Twelve
Thomas C. Hales
This article sketches the proofs of two theorems about sphere packings in Euclidean 3-space. The first is K. Bezdek's strong dodecahedral conjecture: the surface area of every boun…