Edge close ball packings

For a packing of unit balls in R-3, an edge-line is the intersection of the planes of two intersecting faces of some Dirichlet-Voronoi cell, like for example the line of an edge. Now the edge closeness of the arrangement is t he maximal distance between an edge-line for a Dirichlet-Voronoi cell and t he centre of the corresponding unit ball. We show that the unique packing w ith minimal edge closeness is generated by the space centred cubic lattice.