Kynčl, JanSafernova, ZuzanaDíaz Báñez, José MiguelGarijo Royo, DeliaMárquez Pérez, AlbertoUrrutia Galicia, Jorge2017-05-182017-05-182013Kynčl, J. y Safernova, Z. (2013). On the nonexistence of k-reptile simplices in R3 and R4. En XV Spanish Meeting on Computational Geometry, Sevilla.http://hdl.handle.net/11441/60038A d-dimensional simplex S is called a k-reptile (or a k-reptile simplex) if it can be tiled without overlaps by k simplices with disjoint interiors that are all mutually congruent and similar to S. For d=2, triangular k-reptiles exist for many values of k 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 also 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/openAccess