Uniqueness of lattice packings and coverings of extreme density

For d = 2; 3 a generic convex body in E-d has a unique lattice packing and for d >= 4 at most a(d) lattice packings of maximum density, where a (d) >= 1 is a constant. If in E-d a certain connectedness property holds, one may take a(d) = 1. Dually, for d = 2 a generic convex body has a unique lattice covering of minimum density and for d >= 3 there is a constant b(d) >= 1 such that it has at most b(d) such coverings.