A proof of the dodecahedral conjecture

1998/11/11 by Thomas Hales, Hales, Thomas C., Sean McLaughlin +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.math/9811079

openalex publication_date 1998/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.)

Cited by

• Sphere Packings in 3 Dimensions
• Bounding the density of binary sphere packing

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