---
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@
...