In 1994, S. K. Stein and S. Szabo posed a problem concerning simple three-dimensional shapes, known as semicrosses, or tripods. By denition, a tripod is formed by a corner and the three adjacent edges of an integer cube. How densely can one ll the space with non-overlapping tripods of a given size? In particular, is it possible to ll a constant fraction of the space as the tripod size tends to innity? In this paper, we settle the second question in the negative: the fraction of the space that can be lled with tripods of a growing size must be innitely small.