Abstract
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.
Cite
CITATION STYLE
Tiskin, A. (2000). Tripods do not pack densely. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1858, pp. 272–280). Springer Verlag. https://doi.org/10.1007/3-540-44968-x_27
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