The fragile lattice packings of spheres in three-dimensional space

The close-packed-sphere model is often used to explain the frequent occurrence of face-centered cubic lattice structures. Recently, it has been found that in body- centered cubic and body-centered tetragonal lattices the volume of the interstitial void is maximized. In this paper all of the three-dimensional lattice packings of spheres with this property are determined: there are, in addition to the two just mentioned, only the simple cubic and simple hexagonal lattices. A quantitative measure of the relative instability of these packings is also given.