  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 bounded Voronoi cell in a packing of balls of radius 1 is
at least that of a regular dodecahedron of inradius 1. The second theorem is L.
Fejes Toth's contact conjecture, which asserts that in 3-space, any packing of
congruent balls such that each ball is touched by twelve others consists of
hexagonal layers. Both proofs are computer assisted. Complete proofs of these
theorems appear in the author's book "Dense Sphere Packings" and a related
preprint
