  Four mutually tangent spheres form two gaps. In each of these, one can
inscribe in a unique way four mutually tangent spheres such that each one of
these spheres is tangent to exactly three of the original spheres. Repeating
the process gives rise to a generalized Apollonian sphere packing. These
packings have remarkable properties. One of them is the local to global
principle and will be proven in this paper.
