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- W2112820001 abstract "A d-dimensional simplex S is called a k-reptile if it can be tiled without overlaps by simplices S 1,S 2,…,S k that are all mutually congruent, and similar to S. For d=2, k-reptile simplices (triangles) exist for many values of k, and they have been completely characterized by Snover, Waiveris, and Williams. On the other hand, for d≥3, only one construction of k-reptile simplices is known, the Hill simplices, and it provides only k of the form m d , m=2,3,…. We prove that for d=3, k-reptile simplices (tetrahedra) exist only for k=m 3. This partially confirms a conjecture of Hertel, asserting that the only k-reptile tetrahedra are the Hill tetrahedra. Our research has been motivated by the problem of probabilistic packet marking in theoretical computer science, introduced by Adler in 2002." @default.
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- W2112820001 date "2011-03-04" @default.
- W2112820001 modified "2023-09-27" @default.
- W2112820001 title "On the Nonexistence of k-reptile Tetrahedra" @default.
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- W2112820001 doi "https://doi.org/10.1007/s00454-011-9334-z" @default.
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