[{"author":[{"first_name":"Jan","last_name":"Kynčl"},{"last_name":"Patakova","first_name":"Zuzana","orcid":"0000-0002-3975-1683","id":"48B57058-F248-11E8-B48F-1D18A9856A87"}],"dini_type":"doc-type:article","date_updated":"2021-01-12T08:11:28Z","date_created":"2018-12-11T11:48:00Z","volume":24,"publication_status":"published","department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"UlWa"}],"file_date_updated":"2020-07-14T12:47:47Z","publist_id":"6996","creator":{"login":"apreinsp","id":"4435EBFC-F248-11E8-B48F-1D18A9856A87"},"language":[{}],"oa":1,"quality_controlled":"1","month":"07","publication_identifier":{"issn":[]},"pubrep_id":"984","file":[{"access_level":"open_access","file_name":"IST-2018-984-v1+1_Patakova_on_the_nonexistence_of_k-reptile_simplices_in_R_3_and_R_4_2017.pdf","creator":"system","file_size":544042,"content_type":"application/pdf","file_id":"5077","relation":"main_file","checksum":"a431e573e31df13bc0f66de3061006ec","date_created":"2018-12-12T10:14:25Z","date_updated":"2020-07-14T12:47:47Z"}],"oa_version":"Submitted Version","_id":"701","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","ddc":[],"intvolume":" 24","abstract":[{"lang":"eng"}],"issue":"3","type":"journal_article","date_published":"2017-07-14T00:00:00Z","publication":"The Electronic Journal of Combinatorics","citation":{"chicago":"Kynčl, Jan, and Zuzana Patakova. “On the Nonexistence of k Reptile Simplices in ℝ^3 and ℝ^4.” The Electronic Journal of Combinatorics. International Press, 2017.","short":"J. Kynčl, Z. Patakova, The Electronic Journal of Combinatorics 24 (2017) 1–44.","mla":"Kynčl, Jan, and Zuzana Patakova. “On the Nonexistence of k Reptile Simplices in ℝ^3 and ℝ^4.” The Electronic Journal of Combinatorics, vol. 24, no. 3, International Press, 2017, pp. 1–44.","ieee":"J. Kynčl and Z. Patakova, “On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4,” The Electronic Journal of Combinatorics, vol. 24, no. 3. International Press, pp. 1–44, 2017.","apa":"Kynčl, J., & Patakova, Z. (2017). On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4. The Electronic Journal of Combinatorics. International Press.","ista":"Kynčl J, Patakova Z. 2017. On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4. The Electronic Journal of Combinatorics. 24(3), 1–44."},"page":"1-44","day":"14","uri_base":"https://research-explorer.ista.ac.at","has_accepted_license":"1","dc":{"date":["2017"],"language":["eng"],"rights":["info:eu-repo/semantics/openAccess"],"source":["Kynčl J, Patakova Z. On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4. The Electronic Journal of Combinatorics. 2017;24(3):1-44."],"title":["On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4"],"relation":["info:eu-repo/semantics/altIdentifier/issn/10778926"],"subject":["ddc:500"],"publisher":["International Press"],"creator":["Kynčl, Jan","Patakova, Zuzana"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"identifier":["https://research-explorer.ista.ac.at/record/701","https://research-explorer.ista.ac.at/download/701/5077"],"description":["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."]}}]