--- res: bibo_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 a^2, 3a^2 or a^2+b^2 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 = m^d, 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 = m^3. 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 = m^2.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Jan foaf_name: Kynčl, Jan foaf_surname: Kynčl - foaf_Person: foaf_givenName: Zuzana foaf_name: Patakova, Zuzana foaf_surname: Patakova foaf_workInfoHomepage: http://www.librecat.org/personId=48B57058-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-3975-1683 bibo_issue: '3' bibo_volume: 24 dct_date: 2017^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/10778926 dct_language: eng dct_publisher: International Press@ dct_title: On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4@ ...