On large lattice packings of spheres (Q678584)

Let \(B^d\) denote the unit ball in \(E^d\), let \(L\) be a lattice such that \(L+B^d\) is a packing, let \(C_n\) be a set of \(n\) points in \(L\) and let \(P= \text{conv} C_n\). Then \(C_n+ B^d\) is a finite lattice packing with density \(nV(B^d)/V(P+ \rho B^d)\). The author shows that ``\(\dots\) flat or spherelike polytopes \(P\) generate less dense packings, whereas polytopes with suitably large facets generate dense packings. This indicates that large packings in \(E^3\) of high parametric density may be good models for real crystals''.