A new packing density bound in 3-space (Q2572586)

The author shows that every compact convex set \(K\) which is centrally symmetric and has a nonempty interior gives rise to a lattice packing of the Euclidean three dimensional space with density at least \(0.53835\dots\). The packing consists of layers in which plane packings of cross-sections of \(K\) are defined and then uses the corresponding bound for the plane packings. The density is estimated by Minkowski combinations and the Brunn-Minkowski inequality.