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The union of translates of a closed unit n-dimensional cube whose edges are parallel to the coordinate unit vectors e"...,en and whose centers are te,-, |i| < fc, 1 < j' < n, is called a (k, n)-cross. A system of translates of a (fc, n)-cross is called an integer (a rational) lattice tiling if its union is n-space and the interiors of its elements are disjoint, the translates form a lattice and each translation vector of the lattice has integer (rational) coordinates. In this paper we shalldoi:10.1090/s0002-9939-1985-0776181-9 fatcat:c3ldtxkjt5aktfah5oob2wa5cm