Finding the Best Face on a Voronoi Polyhedron: the Strong Dodecahedral Conjecture Revisited

• Autores: Károly Bezdek, Endre Daróczy-Kiss
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 145, Nº 3, 2005, págs. 191-206
• Idioma: inglés
• DOI: 10.1007/s00605-004-0296-6
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• Resumen

  • In this paper we prove the following theorem. The surface area density of a unit ball in any face cone of a Voronoi cell in an arbitrary packing of unit balls of Euclidean 3-space is at most and so the surface area of any Voronoi cell in a packing with unit balls in Euclidean 3-space is at least This result and the ideas of its proof support the Strong Dodecahedral Conjecture according to which the surface area of any Voronoi cell in a packing with unit balls in Euclidean 3-space is at least as large as 16.6508..., the surface area of a regular dodecahedron of inradius 1.