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The notion of densest packing of compact bodies, as introduced by Hilbert, is generalized to the notion of non-completable 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 the number of combinatorially distinct Voronoi-Dirichlet regions in the Euclidean n-space that correspond to the marked points is finite. Bibliography: 5 titles.