FCC versus HCP via parametric density (Q1969799)

The author considers the asymptotic behaviour of finite sphere packings in the face centered cubic lattice (fcc), the hexagonal closest packing (hcp) and related periodic structures called Barlow packings. Their density is measured by parametric density and density deviation and it is shown that asymptotically the shape of a regular octahedron from the fcc-lattice is denser than any other of the considered packings and hence tends faster to be common (infinite) packing density of \(\pi/\sqrt{18}\). So it is a finite contribution to the Kepler conjecture. Further, it coincides with the physical phenomenon that most of the noble gases crystallize in fcc and not in hcp.