ON 2D PACKINGS OF CUBES IN THE TORUS

The 2D packings of cubes (i.e. squares) in the torus T-2 = [0, 1)(2) a re considered. We obtain the exact expression N-2(lambda) = right perp endicular lambda right perpendicular lambda left perpendicular left pe rpendicular for the quantity N-2(lambda), the maximal number of 2D cub es in a packing. (Here 1/lambda is the length of sides of cubes, lambd a is an element of R, lambda > 2.) Corresponding best packings are con structed. Both rank 1 best lattice packings and rank 2 best lattice pa ckings are given.