About: There are only two nonobtuse binary triangulations of the unit n-cube

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About: There are only two nonobtuse binary triangulations of the unit n-cube Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Triangulations of the cube into a minimal number of simplices without additional vertices have been studied by several authors over the past decades. For 3n7 this so-called simplexity of the unit cube In is now known to be 5,16,67,308,1493, respectively. In this paper, we study triangulations of In with simplices that only have nonobtuse dihedral angles. A trivial example is the standard triangulation into n! simplices. In this paper we show that, surprisingly, for each n3 there is essentially only one other nonobtuse triangulation of In, and give its explicit construction. The number of nonobtuse simplices in this triangulation is equal to the smallest integer larger than n!(e-2). Triangulations of the cube into a minimal number of simplices without additional vertices have been studied by several authors over the past decades. For 3n7 this so-called simplexity of the unit cube In is now known to be 5,16,67,308,1493, respectively. In this paper, we study triangulations of In with simplices that only have nonobtuse dihedral angles. A trivial example is the standard triangulation into n! simplices. In this paper we show that, surprisingly, for each n3 there is essentially only one other nonobtuse triangulation of In, and give its explicit construction. The number of nonobtuse simplices in this triangulation is equal to the smallest integer larger than n!(e-2). (en)
Title	There are only two nonobtuse binary triangulations of the unit n-cube There are only two nonobtuse binary triangulations of the unit n-cube (en)
skos:prefLabel	There are only two nonobtuse binary triangulations of the unit n-cube There are only two nonobtuse binary triangulations of the unit n-cube (en)
skos:notation	RIV/67985840:_____/13:00387003!RIV13-AV0-67985840
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(IAA100190803)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Křížek, Michal
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	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	110861
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/13:00387003
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	triangulation; simplexity; nonobtuse simplex (en)
http://linked.open.../riv/klicoveSlovo	triangulation nonobtuse simplex simplexity
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[7B50C3BC14DD]
http://linked.open...i/riv/nazevZdroje	Computational Geometry-Theory and Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	The finite element method for higher dimensional problems
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	46
http://linked.open...iv/tvurceVysledku	Brandts, J. Křížek, Michal Dijkhuis, S. de Haan, V.
http://linked.open...ain/vavai/riv/wos	000312467300009
issn	0925-7721
number of pages	12 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.comgeo.2012.09.005

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