Abstract
The union of translates of a closed unit n n -dimensional cube whose edges are parallel to the coordinate unit vectors e 1 , ⊠, e n {{\mathbf {e}}_1}, \ldots ,{{\mathbf {e}}_n} and whose centers are i e j , | i | †k , 1 †j †n i{{\mathbf {e}}_j},\left | i \right | \leq k,1 \leq j \leq n , is called a ( k , n ) (k,n) -cross. A system of translates of a ( k , n ) (k,n) -cross is called an integer (a rational) lattice tiling if its union is n 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 shall continue the examination of rational cross tilings begun in [2], constructing rational lattice tilings by crosses that have noninteger coordinates on several axes.
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