Continuous deformation of sphere-packing structures extending over simple, body-centered, and face-centered cubic lattices

We have shown the existence of a continuous deformation extending over three spheres-packing structures corresponding to simple cubic, body-centered cubic, and face-centered cubic lattices. Throughout the continuous deformation, each sphere makes contact with at least six spheres, and the entire structure sustains a packing structure. The changes in the packing densities, contact numbers, and space groups caused by the deformation processes are explained in detail.