A property of the normal subdivision of space into polyhedra induced by a packing of compact bodies

The notion of densest packing of compact bodies, as introduced by Hilbert, is generalized to the notion of noncompletable packing of compact bodies. The bodies in the packing are equipped by marked points. Conditions on the arrangement of the marked points in the packing generalize those for the Delone–Aleksandrov point system. It is proved that in the Euclidean $n$-space the number of combinatorially distinct Voronoi–Dirichlet regions corresponding to the marked points is finite.