Hot chocolate effect - Revision history

en>Kumorifox: Undid revision 636104790 by Funandtrvl (talk) This page is physics-related; the focus is not on the beverage at all

2014-12-01T20:30:32Z

Undid revision 636104790 by Funandtrvl (talk) This page is physics-related; the focus is not on the beverage at all

← Older revision		Revision as of 22:30, 1 December 2014
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en>Rderdwien at 00:28, 3 March 2014

2014-03-03T00:28:12Z

← Older revision		Revision as of 02:28, 3 March 2014
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	~~{\| class="wikitable" align="right" style="margin-left:10px" width="250"~~		The person who wrote the article is called Jayson Hirano and he totally digs that title. Office supervising is where her main earnings comes from. To perform lacross is the thing I adore most of all. Her family lives in Ohio but her spouse wants them to transfer.<br><br>My web-site [http://findyourflirt.net/index.php?m=member_profile&p=profile&id=117823 psychic phone]
	~~!bgcolor=#e7dcc3 colspan=2\|Regular octaexon<BR>(7-simplex)~~
	\|-
	\|bgcolor=#ffffff align=center colspan=2\|[[Image:Uniform polytope 3,3,3,3,3,3 t0.jpg\|280px]]<BR>Model created using straws (edges) and plasticine balls (vertices) in [[Triakis tetrahedron\|triakis tetrahedral]] envelope
	\|-
	~~\|bgcolor=#e7dcc3\|Type\|\|Regular [[7-polytope]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Family\|\|[[simplex]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Schläfli symbol]]\|\| {3,3,3,3,3,3}~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Coxeter-Dynkin diagram]]\|\|{{CDD\|\|node_1\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node}}~~
	\|-
	~~\|bgcolor=#e7dcc3\|6-faces\|\|8 [[6-simplex]][[Image:6-simplex_t0.svg\|25px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|5-faces\|\|28 [[5-simplex]][[Image:5-simplex_t0.svg\|25px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|4-faces\|\|56 [[5-cell]][[Image:4-simplex_t0.svg\|25px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Cells\|\|70 [[tetrahedron]][[Image:3-simplex_t0.svg\|25px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Faces\|\|56 [[triangle]][[Image:2-simplex_t0.svg\|25px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Edges\|\|28~~
	\|-
	~~\|bgcolor=#e7dcc3\|Vertices\|\|8~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Vertex figure]]\|\|[[6-simplex]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Petrie polygon]]\|\|[[octagon]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Coxeter group]]\|\| A<sub>7</sub> [3,3,3,3,3,3]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Dual\|\|[[Self-dual polytope\|Self-dual]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Properties\|\|[[Convex polytope\|convex]]~~
	\|}
	~~In [[seven-dimensional space\|7-dimensional]] [[geometry]], a 7-[[simplex]]~~ is a self-dual [[Regular polytope\|regular]] [[7-polytope]]. It has 8 [[vertex (geometry)\|vertices]], 28 [[Edge (geometry)\|edge]]s, 56 triangle [[Face (geometry)\|faces]], 70 tetrahedral [[Cell (mathematics)\|cells]], 56 [[5-cell]] 5-faces, 28 [[5-simplex]] 6-faces, and ~~8 [[6-simplex]] 7-faces~~. ~~Its [[dihedral angle]]~~ is ~~cos<sup>−1</sup>(1/7), or approximately 81.79°~~.

	~~== Alternate names ==~~
	It can also be called an '''octaexon''', or '''octa-7-tope''', as an 8-[[facet (geometry)\|facetted]] polytope in 7-dimensions. The [[5-polytope#A note on generality of terms for n-polytopes and elements\|name]] ''octaexon'' is ~~derived from ''octa'' for eight [[Facet (mathematics)\|facets]] in [[Greek language\|Greek]] and [[exa\|''-ex'']] for having six-dimensional facets, and ''-on''. Jonathan Bowers gives an octaexon~~ the ~~acronym '''oca'''~~.~~<ref>{{KlitzingPolytopes\|polyexa.htm\|7D uniform polytopes (polyexa)\|x3o3o3o3o3o - oca}}</ref>~~

	~~== Coordinates ==~~

	~~The [[Cartesian coordinate]]s of the vertices of an origin-centered regular octaexon having edge length 2 are:~~

	~~:<math>\left(\sqrt{1/28},\ \sqrt{1/21},\ \sqrt{1/15},\ \sqrt{1/10},\ \sqrt{1/6},\ \sqrt{1/3},\ \pm1\right)</math>~~
	~~:<math>\left(\sqrt{1/28},\ \sqrt{1/21},\ \sqrt{1/15},\ \sqrt{1/10},\ \sqrt{1/6},\ -2\sqrt{1/3},\ 0\right)</math>~~
	~~:<math>\left(\sqrt{1/28},\ \sqrt{1/21},\ \sqrt{1/15},\ \sqrt{1/10},\ -\sqrt{3/2},\ 0,\ 0\right)</math>~~
	~~:<math>\left(\sqrt{1/28},\ \sqrt{1/21},\ \sqrt{1/15},\ -2\sqrt{2/5},\ 0,\ 0,\ 0\right)</math>~~
	~~:<math>\left(\sqrt{1/28},\ \sqrt{1/21},\ -\sqrt{5/3},\ 0,\ 0,\ 0,\ 0\right)</math>~~
	~~:<math>\left(\sqrt{1/28},\ -\sqrt{12/7},\ 0,\ 0,\ 0,\ 0,\ 0\right)</math>~~
	~~:<math>\left(-\sqrt{7/4},\ 0,\ 0,\ 0,\ 0,\ 0,\ 0\right)</math>~~

	~~More simply, the vertices of the ''7-simplex'' can be positioned~~ in ~~8-space as permutations of (0,0,0,0,0,0,0,1). This construction is based on [[Facet (geometry)\|facets]] of the [[8-orthoplex]]~~.

	~~== Images ==~~
	~~{{7-simplex Coxeter plane graphs\|t0\|150}}~~

	~~== Related polytopes ==~~
	~~This polytope is a facet in the uniform tessellation [[3 31 honeycomb\|3~~<~~sub~~>31<~~/sub~~>~~]] with [[Coxeter~~-~~Dynkin diagram]]:~~
	~~:{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea\|3a\|nodea}}~~

	~~This polytope is one of 71 [[uniform 7-polytope]]s with A<sub>7</sub> symmetry.~~
	~~{{Octaexon family}}~~

	~~== Notes ==~~
	~~{{reflist}}~~

	~~== External links ==~~
	* {{PolyCell \| urlname = glossary.html\| title = Glossary for hyperspace}}
	* [http://~~www.polytope~~.net/~~hedrondude/topes~~.~~htm Polytopes of Various Dimensions]~~
	* [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]

	~~{{Polytopes}}~~

	~~[[Category:7-polytopes]]~~


	~~{{Geometry-stub}}~~

en>FrescoBot: Bot: standard sections headers and minor changes

2014-01-11T20:16:33Z

Bot: standard sections headers and minor changes

← Older revision		Revision as of 22:16, 11 January 2014
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	~~Alyson Meagher~~ is ~~the name her mothers~~ and ~~fathers gave her but she doesn't like when individuals use her full title~~. ~~My day job~~ is an ~~invoicing officer but I~~'~~ve already applied~~ for ~~another one. As a woman what she really likes~~ is ~~style~~ and ~~she~~'~~s been performing it~~ for ~~quite a while~~. ~~Mississippi is where her home is but real psychics~~ ([~~http~~://~~203.250.78.160~~/~~zbxe~~/~~?document_srl=1792908 203~~.~~250~~.~~78.160~~]~~) her husband desires them to transfer.~~<br><br>~~My blog real~~ [http://~~m-card~~.co.kr/xe/~~mcard_2013_promote01/29877 psychic solutions by lynne~~] ([http://~~cspl~~.~~postech~~.~~ac.kr~~/~~zboard/Membersonly/144571 cspl~~.~~postech.ac.kr~~])		{\| class="wikitable" align="right" style="margin-left:10px" width="250"
			!bgcolor=#e7dcc3 colspan=2\|Regular octaexon<BR>(7-simplex)
			\|-
			\|bgcolor=#ffffff align=center colspan=2\|[[Image:Uniform polytope 3,3,3,3,3,3 t0.jpg\|280px]]<BR>Model created using straws (edges) and plasticine balls (vertices) in [[Triakis tetrahedron\|triakis tetrahedral]] envelope
			\|-
			\|bgcolor=#e7dcc3\|Type\|\|Regular [[7-polytope]]
			\|-
			\|bgcolor=#e7dcc3\|Family\|\|[[simplex]]
			\|-
			\|bgcolor=#e7dcc3\|[[Schläfli symbol]]\|\| {3,3,3,3,3,3}
			\|-
			\|bgcolor=#e7dcc3\|[[Coxeter-Dynkin diagram]]\|\|{{CDD\|\|node_1\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node}}
			\|-
			\|bgcolor=#e7dcc3\|6-faces\|\|8 [[6-simplex]][[Image:6-simplex_t0.svg\|25px]]
			\|-
			\|bgcolor=#e7dcc3\|5-faces\|\|28 [[5-simplex]][[Image:5-simplex_t0.svg\|25px]]
			\|-
			\|bgcolor=#e7dcc3\|4-faces\|\|56 [[5-cell]][[Image:4-simplex_t0.svg\|25px]]
			\|-
			\|bgcolor=#e7dcc3\|Cells\|\|70 [[tetrahedron]][[Image:3-simplex_t0.svg\|25px]]
			\|-
			\|bgcolor=#e7dcc3\|Faces\|\|56 [[triangle]][[Image:2-simplex_t0.svg\|25px]]
			\|-
			\|bgcolor=#e7dcc3\|Edges\|\|28
			\|-
			\|bgcolor=#e7dcc3\|Vertices\|\|8
			\|-
			\|bgcolor=#e7dcc3\|[[Vertex figure]]\|\|[[6-simplex]]
			\|-
			\|bgcolor=#e7dcc3\|[[Petrie polygon]]\|\|[[octagon]]
			\|-
			\|bgcolor=#e7dcc3\|[[Coxeter group]]\|\| A<sub>7</sub> [3,3,3,3,3,3]
			\|-
			\|bgcolor=#e7dcc3\|Dual\|\|[[Self-dual polytope\|Self-dual]]
			\|-
			\|bgcolor=#e7dcc3\|Properties\|\|[[Convex polytope\|convex]]
			\|}
			In [[seven-dimensional space\|7-dimensional]] [[geometry]], a 7-[[simplex]] is a self-dual [[Regular polytope\|regular]] [[7-polytope]]. It has 8 [[vertex (geometry)\|vertices]], 28 [[Edge (geometry)\|edge]]s, 56 triangle [[Face (geometry)\|faces]], 70 tetrahedral [[Cell (mathematics)\|cells]], 56 [[5-cell]] 5-faces, 28 [[5-simplex]] 6-faces, and 8 [[6-simplex]] 7-faces. Its [[dihedral angle]] is cos<sup>−1</sup>(1/7), or approximately 81.79°.

			== Alternate names ==
			It can also be called an '''octaexon''', or '''octa-7-tope''', as an 8-[[facet (geometry)\|facetted]] polytope in 7-dimensions. The [[5-polytope#A note on generality of terms for n-polytopes and elements\|name]] ''octaexon'' is derived from ''octa'' for eight [[Facet (mathematics)\|facets]] in [[Greek language\|Greek]] and [[exa\|''-ex'']] for having six-dimensional facets, and ''-on''. Jonathan Bowers gives an octaexon the acronym '''oca'''.<ref>{{KlitzingPolytopes\|polyexa.htm\|7D uniform polytopes (polyexa)\|x3o3o3o3o3o - oca}}</ref>

			== Coordinates ==

			The [[Cartesian coordinate]]s of the vertices of an origin-centered regular octaexon having edge length 2 are:

			:<math>\left(\sqrt{1/28},\ \sqrt{1/21},\ \sqrt{1/15},\ \sqrt{1/10},\ \sqrt{1/6},\ \sqrt{1/3},\ \pm1\right)</math>
			:<math>\left(\sqrt{1/28},\ \sqrt{1/21},\ \sqrt{1/15},\ \sqrt{1/10},\ \sqrt{1/6},\ -2\sqrt{1/3},\ 0\right)</math>
			:<math>\left(\sqrt{1/28},\ \sqrt{1/21},\ \sqrt{1/15},\ \sqrt{1/10},\ -\sqrt{3/2},\ 0,\ 0\right)</math>
			:<math>\left(\sqrt{1/28},\ \sqrt{1/21},\ \sqrt{1/15},\ -2\sqrt{2/5},\ 0,\ 0,\ 0\right)</math>
			:<math>\left(\sqrt{1/28},\ \sqrt{1/21},\ -\sqrt{5/3},\ 0,\ 0,\ 0,\ 0\right)</math>
			:<math>\left(\sqrt{1/28},\ -\sqrt{12/7},\ 0,\ 0,\ 0,\ 0,\ 0\right)</math>
			:<math>\left(-\sqrt{7/4},\ 0,\ 0,\ 0,\ 0,\ 0,\ 0\right)</math>

			More simply, the vertices of the ''7-simplex'' can be positioned in 8-space as permutations of (0,0,0,0,0,0,0,1). This construction is based on [[Facet (geometry)\|facets]] of the [[8-orthoplex]].

			== Images ==
			{{7-simplex Coxeter plane graphs\|t0\|150}}

			== Related polytopes ==
			This polytope is a facet in the uniform tessellation [[3 31 honeycomb\|3<sub>31</sub>]] with [[Coxeter-Dynkin diagram]]:
			:{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea\|3a\|nodea}}

			This polytope is one of 71 [[uniform 7-polytope]]s with A<sub>7</sub> symmetry.
			{{Octaexon family}}

			== Notes ==
			{{reflist}}

			== External links ==
			* {{PolyCell \| urlname = glossary.html\| title = Glossary for hyperspace}}
			* [http://www.polytope.net/hedrondude/topes.htm Polytopes of Various Dimensions]
			* [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]

			{{Polytopes}}

			[[Category:7-polytopes]]


			{{Geometry-stub}}

en>TheAMmollusc: Successfully de-orphaned! Wikiproject Orphanage: You can help! (it already seems to have 3 links)

2012-08-23T11:01:44Z

Successfully de-orphaned! Wikiproject Orphanage: You can help! (it already seems to have 3 links)

New page

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