Resumen de Finding the Best Face on a Voronoi Polyhedron: the Strong Dodecahedral Conjecture Revisited
Károly Bezdek, Endre Daróczy-Kiss
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.
