Timeline of mathematics - Revision history

en>Hroðulf: /* Before 1000 BC */ fixed red link, added locations, summarize content of Chou Pei Suan Ching

2015-01-09T09:53:03Z

Before 1000 BC: fixed red link, added locations, summarize content of Chou Pei Suan Ching

← Older revision		Revision as of 11:53, 9 January 2015
Line 1:		Line 1:
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en>Leoberacai: /* 1st millennium AD */

2014-02-25T23:03:01Z

1st millennium AD

← Older revision		Revision as of 01:03, 26 February 2014
Line 1:		Line 1:
	~~{{DISPLAYTITLE:2<sub><span style="display:none"> </span>51</sub> honeycomb}}~~		If an existing Word - Press code is found vulnerable, Word - Press will immediately issue an update for that. Also, you may want to opt for a more professioanl theme if you are planning on showing your site off to a high volume of potential customers each day. SEO Ultimate - I think this plugin deserves more recognition than it's gotten up till now. 2- Ask for the designs and graphics that will be provided along with the Word - Press theme. The number of options offered here is overwhelming, but once I took the time to begin to review the video training, I was amazed at how easy it was to create a squeeze page and a membership site. <br><br>These folders as well as files have to copied and the saved. The higher your blog ranks on search engines, the more likely people will find your online marketing site. You are able to set them within your theme options and so they aid the search engine to get a suitable title and description for the pages that get indexed by Google. This is identical to doing a research as in depth above, nevertheless you can see various statistical details like the number of downloads and when the template was not long ago updated. Once you've installed the program you can quickly begin by adding content and editing it with features such as bullet pointing, text alignment and effects without having to do all the coding yourself. <br><br>Photography is an entire activity in itself, and a thorough discovery of it is beyond the opportunity of this content. It was also the very first year that the category of Martial Arts was included in the Parents - Connect nationwide online poll, allowing parents to vote for their favorite San Antonio Martial Arts Academy. If you have any kind of inquiries relating to where and how you can utilize [http://www.shortlinki.com/wordpress_dropbox_backup_2173312 wordpress backup plugin], you can call us at our own internet site. You can now search through the thousands of available plugins to add all kinds of functionality to your Word - Press site. User friendly features and flexibility that Word - Press has to offer is second to none. Socrates: (link to ) Originally developed for affiliate marketers, I've used this theme again and again to develop full-fledged web sites that include static pages, squeeze pages, and a blog. <br><br>Word - Press installation is very easy and hassle free. php file in the Word - Press root folder and look for this line (line 73 in our example):. Websites that do rank highly, do so becaue they use keyword-heavy post titles. There are many advantages of hiring Wordpress developers for Wordpress project development:. The popularity of Word - Press has increased the demand for Word - Press themes and these themes sells like hot cake on the internet. <br><br>A sitemap is useful for enabling web spiders and also on rare occasions clients, too, to more easily and navigate your website. s ability to use different themes and skins known as Word - Press Templates or Themes. The days of spending a lot of time and money to have a website built are long gone. Change the entire appearance of you blog using themes with one click. 95, and they also supply studio press discount code for their clients, coming from 10% off to 25% off upon all theme deals.
	~~{\| class="wikitable" align="right" style="margin~~-~~left:10px" width="280"~~
	~~!bgcolor=#e7dcc3 colspan=2\|2<sub>51</sub> honeycomb~~
	\|-
	~~\|bgcolor=#ffffff align=center colspan=2\|(No image)~~
	\|-
	~~\|bgcolor=#e7dcc3\|Type\|\|[[9-polytope#Regular_and_uniform_honeycombs\|Uniform tessellation]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Family\|\|[[Uniform 2 k1 polytope\|2<sub>k1</sub> polytope]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Schläfli symbol]]\|\| {3,3~~,~~3<sup>5,1</sup>}~~
	\|-
	~~\|bgcolor=#e7dcc3\|Coxeter symbol\|\| 2<sub>51</sub>~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Coxeter-Dynkin diagram]]\|\|{{CDD\|nodea_1\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea\|3a\|nodea\|3a\|nodea\|3a\|nodea}}~~
	\|-
	~~\|bgcolor=#e7dcc3\|8-face types\|\|'''[[2 41 polytope\|2<sub>41</sub>]]'''[[File:Gosset 2 41 petrie~~.~~svg\|25px]]<BR>[[8-simplex\|{3<sup>7</sup>}]][[Image:8-simplex t0~~.~~svg\|25px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|7~~-~~face types\|\|~~'~~''[[2 31 polytope\|2<sub>31</sub>]]'''[[Image:Gosset 2 31 polytope.svg\|25px]]<BR>[[7-simplex\|{3<sup>6</sup>}]][[Image:7-simplex t0~~.~~svg\|25px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|6-face types\|\|'''[[2 21 polytope\|~~2~~<sub>21</sub>]]'''[[Image:E6 graph.svg\|25px]]<BR>[[6~~-~~simplex\|{3<sup>5</sup>}]][[Image:6~~-~~simplex t0~~.~~svg\|25px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|5-face types\|\|'''[[5-orthoplex\|2<sub>11</sub>]]'''[[Image:Cross graph 5~~.~~svg\|25px]]~~<BR>~~[[5-simplex\|{3~~<~~sup~~>~~4</sup>}]][[Image:5-simplex t0~~.~~svg\|25px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|4-face type\|\|[[5-cell\|{3<sup>3</sup>}]][[Image:4-simplex t0.svg\|25px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Cells\|\|[[tetrahedron\|{3<sup>2</sup>}]][[Image:3-simplex t0.svg\|25px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Faces\|\|[[triangle\|{3}]][[Image:2-simplex t0.svg\|25px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Edge figure]]\|\|'''[[rectified 6-simplex\|0<sub>51</sub>]]''' [[File:6-simplex t1.svg\|30px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Vertex figure]]\|\|'''[[8-demicube\|1<sub>51</sub>]]''' [[File:8-demicube.svg\|30px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Edge figure]]\|\|'''[[Rectified 7-simplex\|0<sub>51</sub>]]''' [[File:7-simplex t1.svg\|30px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Coxeter group]]\|\|<math>{\tilde{E}}_8</math>, [3<sup>5,2,1</sup>]~~
	\|}
	~~In 8-dimensional [[geometry]]~~, the ~~'''2<sub>51</sub>''' honeycomb is a space-filling [[uniform tessellation]]~~. ~~It is composed of [[Gosset 2 41 polytope\|2<sub>41</sub> polytope]]~~ and ~~[[8-simplex]] [[Facet (geometry)\|facets]] arranged in~~ a ~~[[8-demicube]] [[vertex figure]]. It is~~ the ~~final figure in the [[uniform 2 k1 polytope\|2<sub>k1</sub> family]]~~.

	~~==Construction==~~

	It is ~~created by~~ a ~~[[Wythoff construction]] upon a set of 9 [[hyperplane]] mirrors~~ in ~~8-dimensional space.~~

	~~The facet information~~ can ~~be extracted from its [[Coxeter-Dynkin diagram]].~~
	~~: {{CDD\|nodea_1\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea\|3a\|nodea\|3a\|nodea\|3a\|nodea}}~~

	~~Removing~~ the ~~node on~~ the ~~short branch leaves the [[8-simplex]]~~.
	~~: {{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|nodea\|3a\|nodea\|3a\|nodea\|3a\|nodea\|3a\|nodea}}~~

	~~Removing~~ the ~~node on~~ the ~~end of the 5-length branch leaves the [[Gosset 2 41 polytope\|2~~<~~sub~~>41<~~/sub~~>~~]].~~
	~~: {{CDD\|nodea_1\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea\|3a\|nodea\|3a\|nodea}}~~

	~~The [[vertex figure]]~~ is ~~determined by removing the ringed node~~ and ~~ringing~~ the ~~neighboring node~~. ~~This makes~~ the ~~[[8-demicube]], 1<sub>51</sub>.~~
	~~: {{CDD\|nodea_1\|3a\|branch\|3a\|nodea\|3a\|nodea\|3a\|nodea\|3a\|nodea\|3a\|nodea}}~~

	~~The [[edge figure]] is~~ the ~~vertex figure~~ of the ~~vertex figure. This makes the [[rectified 7~~-~~simplex]]~~, ~~0<sub>51</sub>~~.
	~~: {{CDD\|branch_10\|3a\|nodea\|3a\|nodea\|3a\|nodea\|3a\|nodea\|3a\|nodea}}~~

	~~{{-}}~~

	~~== Related polytopes~~ and ~~honeycombs==~~
	~~{{2 k1 polytopes}}~~

	~~== See also ==~~
	* [~~[5 21 honeycomb\|5<sub>21<~~/~~sub> honeycomb]]~~
	* [[1 52 honeycomb\|1<sub>52</~~sub> honeycomb~~]]

	~~==References==~~
	* [[Harold Scott MacDonald Coxeter\|Coxeter]] ''The Beauty of ~~Geometry: Twelve Essays'', Dover Publications, 1999, ISBN 978~~-0-~~486-40919-1 (Chapter 3~~: ~~Wythoff's Construction for Uniform Polytopes)~~
	* [[Harold Scott MacDonald Coxeter\|Coxeter]] ''Regular Polytopes'' (~~1963~~), ~~Macmillian Company~~
	** ''Regular Polytopes'', ~~Third edition~~, ~~(1973), Dover edition, ISBN 0~~-~~486~~-~~61480-8~~ (~~Chapter 5: The Kaleidoscope~~)
	* '''Kaleidoscopes: ~~Selected Writings of H.S.M~~. ~~Coxeter'''~~, ~~edited by F~~. ~~Arthur Sherk, Peter McMullen, Anthony C~~. ~~Thompson, Asia Ivic Weiss, Wiley~~-~~Interscience Publication~~, ~~1995~~, ~~ISBN 978-0-471-01003-6 [http://www~~.~~wiley.com/WileyCDA/WileyTitle/productCd~~-~~0471010030~~.~~html]~~
	** (Paper 24) H.S.~~M. Coxeter~~, ~~''Regular~~ and ~~Semi-Regular Polytopes III''~~, ~~[Math. Zeit~~. ~~200 (1988) 3-45]~~

	~~{{Honeycombs}}~~

	~~[[Category:9-polytopes]]~~


	~~{{geometry-stub}}~~

en>K9re11: /* 20th century */

2014-01-30T14:53:25Z

20th century

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115.74.129.63: /* 21st century */

2012-08-27T13:56:55Z

21st century

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