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On the nonexistence of k-reptile simplices in R 3 and R 4 ∗
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kyncl, Jan Patáková, Zuzana |
| Copyright Year | 2017 |
| Abstract | A d-dimensional simplex S is called a k-reptile (or a k-reptile simplex ) if it can be tiled by k simplices with disjoint interiors that are all mutually congruent and similar to S. For d = 2, triangular k-reptiles exist for all k of the form a2, 3a2 or a2 + b2 and they have been completely characterized by Snover, Waiveris, and Williams. On the other hand, the only k-reptile simplices that are known for d > 3, have k = md, where m is a positive integer. We substantially simplify the proof by Matoušek and the second author that for d = 3, k-reptile tetrahedra can exist only for k = m3. We then prove a weaker analogue of this result for d = 4 by showing that four-dimensional k-reptile simplices can exist only for k = m2. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.combinatorics.org/ojs/index.php/eljc/article/download/v24i3p1/pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
