Combinatorial packings of by certain error spheres

This paper concerns one of the "error spheres" discussed by Golomb in 1969, his "Stein corner" in three-dimensional Euclidean space . This figure, which we shall call a semicross, is defined as follows. Let be a positive integer. The -semicross consists of unit cubes: a corner cube together with three nonopposite arms of length . (It may be thought of as a tripod.) For translates of the -semicross do not tile . The question of how densely the translates pack will be examined by combinatorial techniques. While the maximum density is not determined, sufficiently dense packings are produced to show that they are much denser than the densest lattice packing.