Abstract
This paper concerns one of the error spheres discussed by Golomb in 1969, his Stein in three-dimensional Euclidean space R^{3} . This figure, which we shall call a semicross, is defined as follows. Let k be a positive integer. The (k, 3) -semicross consists of 3k + 1 unit cubes: a corner cube together with three nonopposite arms of length k . (It may be thought of as a tripod.) For k \geq 2 translates of the (k, 3) -semicross do not tile R^{3} . The question of how densely the translates pack R^{3} 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.
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