Tacit collusion - Revision history

en>Yobot: Tagging using AWB (10703)

2015-01-07T11:49:27Z

Tagging using AWB (10703)

← Older revision		Revision as of 13:49, 7 January 2015
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	~~Nice to meet you, my name is Figures Held though~~ I ~~don~~'t ~~really~~ like ~~being known as like that. To do aerobics is a factor that I'm completely addicted~~ [http://~~wixothek~~.com~~/blog/557 at home std testing] home [http://Www~~.~~askdoctork.com~~/~~what-should-i-know-about-living-with-genital-herpes-201211073624 std testing] to. Hiring has been my [http://www.noonptm.com/fox/upload/index~~.php?do=~~/profile-3715/info/ home~~ std test ~~kit~~] ~~profession for some time~~ but I'~~ve currently utilized~~ for ~~another 1~~. ~~Her husband and her reside in Puerto Rico~~ but ~~she will have~~ to move ~~1 working day or an additional~~.~~<br><br>Also visit~~ my ~~web over the counter std test page - std home test ([http://www~~.~~pponline.co.uk/user/miriamlinswkucrd mouse click the following internet site])~~		I am Oscar and I totally dig that title. His spouse doesn't like it [http://citymama.com.ua/profile_info.php?ID=38588 over the counter std test] way he does but what he truly likes performing is to do aerobics and he's been performing it for quite a while. Minnesota has usually been his home but his spouse desires them to move. Bookkeeping is my profession.

en>Cmanser: /* Forms */

2014-02-24T09:42:11Z

Forms

← Older revision		Revision as of 11:42, 24 February 2014
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	~~[[Image:Polyhedral schlegel diagrams.svg\|thumb\|Examples colored by the number of sides on each face. Yellow [[triangle]]s, red [[Square (geometry)\|squares]], and green [[pentagon]]s.]]~~		Nice to meet you, my name is Figures Held though I don't really like being known as like that. To do aerobics is a factor that I'm completely addicted [http://wixothek.com/blog/557 at home std testing] home [http://Www.askdoctork.com/what-should-i-know-about-living-with-genital-herpes-201211073624 std testing] to. Hiring has been my [http://www.noonptm.com/fox/upload/index.php?do=/profile-3715/info/ home std test kit] profession for some time but I've currently utilized for another 1. Her husband and her reside in Puerto Rico but she will have to move 1 working day or an additional.<br><br>Also visit my web over the counter std test page - std home test ([http://www.pponline.co.uk/user/miriamlinswkucrd mouse click the following internet site])
	~~[[Image:Hypercube.svg\|thumb\|A [[tesseract]] projected into 3-space as a Schlegel diagram. There are 8 cubic cells visible, one in the center, one below each of the six exterior faces~~, ~~and the last one~~ is '~~'inside-out'' representing the space outside the cubic boundary.]]~~
	In [[geometry]], a '''Schlegel diagram''' is a projection of a [[polytope]] from <math>R^d</math> into <math>R^{d-1}</math> through a point beyond one of its facets. The resulting entity is a [[polytopal subdivision]] of the facet in <math>R^{d-1}</math> that ~~is combinatorially equivalent to the original polytope~~. ~~In 1886 [[Victor Schlegel]] introduced this tool for studying combinatorial and topological properties of polytopes. In dimensions 3 and 4, a Schlegel diagram~~ is a projection of a [[polyhedron]] into a plane figure and a projection of a [[polychoron]] to [[3-space]], respectively. As such, Schlegel diagrams are commonly used as a means of visualizing four-dimensional polytopes.

	~~==Construction==~~

	A Schlegel diagram can be constructed by a [[perspective projection]] viewed from a point outside of the polytope, above the center of a [[Facet (mathematics)\|facet]]. All vertices and edges of the polytope are projected onto a hyperplane of that ~~facet. If the polytope is convex, a point near the facet will exist which maps the facet outside, and all other facets inside, so no edges need to cross in the projection.~~

	~~== Examples ==~~
	~~{\| class=wikitable width=400~~
	~~![[Dodecahedron]]~~
	~~![[120-cell\|Dodecaplex]]~~
	\|-
	~~\|valign=top\|[[Image:Dodecahedron schlegel diagram.png\|200px]]<BR>12 pentagon faces in the plane~~
	~~\|valign=top\|[[Image:Schlegel wireframe 120-cell.png\|200px]]<BR>120 dodecahedral cells in 3-space~~
	\|}

	~~== See also ==~~
	* [[Net (polyhedron)]] – A different approach for visualization by lowering the dimension of a [[polytope]] is to build a net, disconnecting [[facet]]s, and '~~'unfolding'' until the facets can exist on a single [[hyperplane]]. This maintains the geometric scale and shape, but makes the topological connections harder to see.~~

	~~== References ==~~
	* [[Victor Schlegel]] (1883) ''Theorie der homogen zusammengesetzten Raumgebilde'', Nova Acta, Ksl. Leop.-Carol. Deutsche Akademie der Naturforscher, Band XLIV, Nr. 4, Druck von E. Blochmann & Sohn in Dresden. [http://~~www~~.~~citr.auckland.ac.nz~~/~~dgt~~/~~Publications.php?id=544~~]
	* Victor Schlegel (1886) ''Ueber Projectionsmodelle der regelmässigen vier-dimensionalen Körper'', Waren.
	* [~~[Coxeter\|Coxeter, H~~.S.~~M.]]; ''[[Regular Polytopes (book)\|Regular Polytopes]]'', (Methuen and Co., 1948). (p. 242)~~
	** ''[[Regular Polytopes (book)\|Regular Polytopes]]'', (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8
	* {{Citation \| last=Grünbaum \| first=Branko \| authorlink=Branko Grünbaum\| title = Convex polytopes \| location=New York & London \| publisher=[[Springer-Verlag]] \| year=2003 \| isbn=0-~~387-00424-6 \| edition=2nd \| editor1~~-~~first=Volker \| editor1~~-~~last=Kaibel \| editor2~~-~~first=Victor \| editor2~~-~~last=Klee \| editor2~~-~~link=Victor Klee \| editor3~~-~~first=Günter M. \| editor3~~-~~last =Ziegler \| editor3~~-~~link = Günter M~~. ~~Ziegler}}.~~

	~~== External links ==~~
	~~{{Commons category\|Schlegel diagrams}}~~
	* {{mathworld \| urlname = SchlegelGraph ~~\| title = Schlegel graph}}~~
	** {{mathworld \| urlname = Skeleton \| title = Skeleton}}
	* [http://www.~~georgehart~~.com/~~hyperspace~~/~~hart~~-~~120-cell~~.~~html George W~~. ~~Hart: 4D Polytope Projection Models by 3D Printing]~~
	* [http://www.~~nrich~~.~~maths~~.~~org~~/~~public~~/~~viewer.php?obj_id=897 Nrich maths – for~~ the ~~teenager. Also useful for teachers.]~~

	~~[[Category:Polytopes]~~]

194.73.225.194 at 17:29, 11 January 2014

2014-01-11T17:29:56Z

← Older revision		Revision as of 19:29, 11 January 2014
Line 1:		Line 1:
	~~Emilia Shryock~~ is ~~my name but you~~ can ~~call me something you like~~. ~~She~~ is a ~~librarian~~ but ~~she~~'~~s always needed her personal company~~. ~~California is where her~~ [http://www.~~pponline~~.co.uk/~~user~~/~~miriamlinswkucrd at home std test~~] ~~is but she requirements to move simply because of her family~~. ~~What I love performing is doing ceramics but I haven~~'~~t made a dime with it~~.		[[Image:Polyhedral schlegel diagrams.svg\|thumb\|Examples colored by the number of sides on each face. Yellow [[triangle]]s, red [[Square (geometry)\|squares]], and green [[pentagon]]s.]]
			[[Image:Hypercube.svg\|thumb\|A [[tesseract]] projected into 3-space as a Schlegel diagram. There are 8 cubic cells visible, one in the center, one below each of the six exterior faces, and the last one is ''inside-out'' representing the space outside the cubic boundary.]]
			In [[geometry]], a '''Schlegel diagram''' is a projection of a [[polytope]] from <math>R^d</math> into <math>R^{d-1}</math> through a point beyond one of its facets. The resulting entity is a [[polytopal subdivision]] of the facet in <math>R^{d-1}</math> that is combinatorially equivalent to the original polytope. In 1886 [[Victor Schlegel]] introduced this tool for studying combinatorial and topological properties of polytopes. In dimensions 3 and 4, a Schlegel diagram is a projection of a [[polyhedron]] into a plane figure and a projection of a [[polychoron]] to [[3-space]], respectively. As such, Schlegel diagrams are commonly used as a means of visualizing four-dimensional polytopes.

			==Construction==

			A Schlegel diagram can be constructed by a [[perspective projection]] viewed from a point outside of the polytope, above the center of a [[Facet (mathematics)\|facet]]. All vertices and edges of the polytope are projected onto a hyperplane of that facet. If the polytope is convex, a point near the facet will exist which maps the facet outside, and all other facets inside, so no edges need to cross in the projection.

			== Examples ==
			{\| class=wikitable width=400
			![[Dodecahedron]]
			![[120-cell\|Dodecaplex]]
			\|-
			\|valign=top\|[[Image:Dodecahedron schlegel diagram.png\|200px]]<BR>12 pentagon faces in the plane
			\|valign=top\|[[Image:Schlegel wireframe 120-cell.png\|200px]]<BR>120 dodecahedral cells in 3-space
			\|}

			== See also ==
			* [[Net (polyhedron)]] – A different approach for visualization by lowering the dimension of a [[polytope]] is to build a net, disconnecting [[facet]]s, and ''unfolding'' until the facets can exist on a single [[hyperplane]]. This maintains the geometric scale and shape, but makes the topological connections harder to see.

			== References ==
			* [[Victor Schlegel]] (1883) ''Theorie der homogen zusammengesetzten Raumgebilde'', Nova Acta, Ksl. Leop.-Carol. Deutsche Akademie der Naturforscher, Band XLIV, Nr. 4, Druck von E. Blochmann & Sohn in Dresden. [http://www.citr.auckland.ac.nz/dgt/Publications.php?id=544]
			* Victor Schlegel (1886) ''Ueber Projectionsmodelle der regelmässigen vier-dimensionalen Körper'', Waren.
			* [[Coxeter\|Coxeter, H.S.M.]]; ''[[Regular Polytopes (book)\|Regular Polytopes]]'', (Methuen and Co., 1948). (p. 242)
			** ''[[Regular Polytopes (book)\|Regular Polytopes]]'', (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8
			* {{Citation \| last=Grünbaum \| first=Branko \| authorlink=Branko Grünbaum\| title = Convex polytopes \| location=New York & London \| publisher=[[Springer-Verlag]] \| year=2003 \| isbn=0-387-00424-6 \| edition=2nd \| editor1-first=Volker \| editor1-last=Kaibel \| editor2-first=Victor \| editor2-last=Klee \| editor2-link=Victor Klee \| editor3-first=Günter M. \| editor3-last =Ziegler \| editor3-link = Günter M. Ziegler}}.

			== External links ==
			{{Commons category\|Schlegel diagrams}}
			* {{mathworld \| urlname = SchlegelGraph \| title = Schlegel graph}}
			** {{mathworld \| urlname = Skeleton \| title = Skeleton}}
			* [http://www.georgehart.com/hyperspace/hart-120-cell.html George W. Hart: 4D Polytope Projection Models by 3D Printing]
			* [http://www.nrich.maths.org/public/viewer.php?obj_id=897 Nrich maths – for the teenager. Also useful for teachers.]

			[[Category:Polytopes]]

90.207.145.247: /* Duopoly Example */ spelling

2012-03-26T10:02:07Z

Duopoly Example: spelling

New page

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