Interstitial space in hardsphere clusters

The interstitial space in a cluster of spheres is examined to determine the largest sphere that can be placed in its voids. A method is given for obtaining the interstitial sphere belonging to a group of arbitrarily arranged spheres by examining tetrahedral configurations. Given the coordinates of the centers and the radii of the spheres of a tetrahedral group, the coordinates and radius of the tetrahedral interstitial sphere can be found. The method can be applied to interstices of any coordination number. It is applicable to sphere packings with or without crystallographic symmetry.