Dense packings of hard spheres of different sizes based on filling interstices in uniform three-dimensional tilings.

A systematic survey is presented of the maximum packing fractions obtained by decorating the 28 uniform tilings of three-dimensional space with spheres of one size and then filling the interstices of these tilings, starting with the largest, with spheres of different sizes. A number of size ratios and structures are identified that have not, to date, been considered in problems involving the packing of spheres of different sizes.