About: On the nonexistence of k-reptile tetrahedra

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1007/s00454-011-9334-z
Description	A d-dimensional simplex S is called a k-reptile if it can be tiled without overlaps by simplices S_1, S_2,..., S_k that are all congruent and similar to S. For d=2, k-reptile simplices (triangles) exist for many values of k and they have been completely characterized by Snover, Waiveris, and Williams. On the other hand, for d greater than 2, only one construction of k-reptile simplices is known, the Hill simplices, and it provides only k of the form m^d, m = 2, 3,.... We prove that for d greater than 2, k-reptile simplices (tetrahedra) exist only for k=m^3. This partially confirms a conjecture of Hertel, asserting that the only k-reptile tetrahedra are the Hill tetrahedra. A d-dimensional simplex S is called a k-reptile if it can be tiled without overlaps by simplices S_1, S_2,..., S_k that are all congruent and similar to S. For d=2, k-reptile simplices (triangles) exist for many values of k and they have been completely characterized by Snover, Waiveris, and Williams. On the other hand, for d greater than 2, only one construction of k-reptile simplices is known, the Hill simplices, and it provides only k of the form m^d, m = 2, 3,.... We prove that for d greater than 2, k-reptile simplices (tetrahedra) exist only for k=m^3. This partially confirms a conjecture of Hertel, asserting that the only k-reptile tetrahedra are the Hill tetrahedra. (en)
Title	On the nonexistence of k-reptile tetrahedra On the nonexistence of k-reptile tetrahedra (en)
skos:prefLabel	On the nonexistence of k-reptile tetrahedra On the nonexistence of k-reptile tetrahedra (en)
skos:notation	RIV/00216208:11320/11:10100601!RIV12-MSM-11320___
http://linked.open...avai/predkladatel	Matematicko-fyzikální fakulta
http://linked.open...avai/riv/aktivita	P S Z
http://linked.open...avai/riv/aktivity	P(1M0545), S, Z(MSM0021620838)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Matoušek, Jiří Safernová, Zuzana
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	218244
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/11:10100601
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	tetrahedra; k-reptile; nonexistence (en)
http://linked.open.../riv/klicoveSlovo	k-reptile nonexistence tetrahedra
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[2DC31D844180]
http://linked.open...i/riv/nazevZdroje	Discrete and Computational Geometry
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Institute for Theoretical Computer Science
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	46
http://linked.open...iv/tvurceVysledku	Matoušek, Jiří Safernová, Zuzana
http://linked.open...ain/vavai/riv/wos	000294011700012
http://linked.open...n/vavai/riv/zamer	Moderní metody, struktury a systémy informatiky
issn	0179-5376
number of pages	11 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s00454-011-9334-z
http://localhost/t...ganizacniJednotka	11320
is http://linked.open...avai/riv/vysledek of	On the nonexistence of k-reptile tetrahedra On the nonexistence of k-reptile tetrahedra

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