New Periodic Close Packings of Identical Spheres

Abstract

I DESCRIBE here very briefly eleven new periodic close packings of identical spheres. Current literature cites (at most) six, which are: “diamond”, (β-ZnS (“wurtzite”), Cubic-P, Cubic-I, Cubic-F and hexagonal closest packed (h.c.p.)—the first two having the (same) lowest packing ratios and four-fold coordination and the last two the (same) highest-possible packing ratios and twelve-fold coordination. The two notations (Table 1, columns 1 and 2) should be fairly obvious when related to the “old” packings. The detailed consideration of, for example, high planar densities, “continuous deformation” and spherical voids has been omitted here.