On the Nonexistence of k-reptile Tetrahedra

@article{Matousek2011OnTN,
  title={On the Nonexistence of k-reptile Tetrahedra},
  author={J. Matousek and Zuzana Safernov{\'a}},
  journal={Discrete \& Computational Geometry},
  year={2011},
  volume={46},
  pages={599-609}
}
A d-dimensional simplex S is called a k-reptile if it can be tiled without overlaps by simplices S1,S2,…,Sk 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 md, m=2,3,….We prove that for d=3, k-reptile simplices… Expand
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