Invariants of partitions of Rn by identical cubes

This article proves the following proposition: For any partition ⁿ, by congruent n-dimensional cubes, each cube has each of its vertices in contact with vertices of some other cube.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 196, pp. 117–121, 1991.