Algebraic theory of brick packing I

The general theory developed in an earlier paper [1] is applied to solve the problem of packing a region of n-dimensional space with rectangular bricks. When both positive and negative bricks are allowed, a complete solution is obtained for regions of arbitrary shape, while for packings with positive bricks only, a solution is given for sufficiently large rectangular boxes. Partial packings are also considered, and an asymptotic estimate is obtained for the wasted volume in the most efficient packing of a large box with a given set of bricks.