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Journal of the American Mathematical Society

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The dodecahedral conjecture
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by Thomas C. Hales and Sean McLaughlin PDF
J. Amer. Math. Soc. 23 (2010), 299-344 Request permission


This article gives a summary of a proof of Fejes Tóth’s dodecahedral conjecture: the volume of a Voronoi polyhedron in a three-dimensional packing of balls of unit radius is at least the volume of a regular dodecahedron of unit inradius.
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Additional Information
  • Thomas C. Hales
  • Affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, Pennsylvania 15260
  • Email:
  • Sean McLaughlin
  • Affiliation: Department of Mathematics, Carnegie Mellon University, Wean Hall 6113, Pittsburgh, Pennsylvania 15213
  • Email:
  • Received by editor(s): November 19, 1998
  • Published electronically: October 27, 2009
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 23 (2010), 299-344
  • MSC (2010): Primary 52C17
  • DOI:
  • MathSciNet review: 2601036