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| {{DISPLAYTITLE:1<sub><span style="display:none"> </span>52</sub> honeycomb}}
| | I'm Woodrow (25) from Restoule, Canada. <br>I'm learning French literature at a local high school and I'm just about to graduate.<br>I have a part time job in a university.<br><br>Here is my web blog: [http://Ezinearticles.com/?Special-Things-To-Know-About-Psychic-Mediums&id=8624860 want talk psychic] |
| {| class="wikitable" align="right" style="margin-left:10px" width="280"
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| !bgcolor=#e7dcc3 colspan=2|1<sub>52</sub> honeycomb
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| |bgcolor=#ffffff align=center colspan=2|(No image)
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| |bgcolor=#e7dcc3|Type||[[9-polytope#Regular_and_uniform_honeycombs|Uniform tessellation]]
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| |bgcolor=#e7dcc3|Family||[[Uniform 1 k2 polytope|1<sub>k2</sub> polytope]]
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| |bgcolor=#e7dcc3|[[Schläfli symbol]]|| {3,3<sup>5,2</sup>}
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| |bgcolor=#e7dcc3|Coxeter symbol|| 1<sub>52</sub>
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| |bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]||{{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
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| |bgcolor=#e7dcc3|8-face types||'''[[1 42 polytope|1<sub>42</sub>]]'''[[File:Gosset 1 42 polytope petrie.svg|25px]]<BR>'''[[8-demicube|1<sub>51</sub>]]'''[[Image:Demiocteract ortho petrie.svg|25px]]
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| |bgcolor=#e7dcc3|7-face types||'''[[1 32 polytope|1<sub>32</sub>]]'''[[File:Gosset 1 32 petrie.svg|25px]]<BR>'''[[7-demicube|1<sub>41</sub>]]'''[[Image:Demihepteract ortho petrie.svg|25px]]
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| |bgcolor=#e7dcc3|6-face types||'''[[1 22 polytope|1<sub>22</sub>]]'''[[Image:Gosset 1 22 polytope.svg|25px]]<BR>[[6-demicube|{3<sup>1,3,1</sup>}]][[Image:Demihexeract ortho petrie.svg|25px]]<BR>[[6-simplex|{3<sup>5</sup>}]][[Image:6-simplex t0.svg|25px]]
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| |bgcolor=#e7dcc3|5-face types||'''[[5-demicube|1<sub>21</sub>]]'''[[Image:Demipenteract graph ortho.svg|25px]]<BR>[[5-simplex|{3<sup>4</sup>}]][[Image:5-simplex t0.svg|25px]]
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| |bgcolor=#e7dcc3|4-face type||'''[[16-cell|1<sub>11</sub>]]'''[[Image:Cross graph 4.svg|25px]]<BR>[[5-cell|{3<sup>3</sup>}]][[Image:4-simplex t0.svg|25px]]
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| |bgcolor=#e7dcc3|Cells||[[tetrahedron|{3<sup>2</sup>}]][[Image:3-simplex t0.svg|25px]]
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| |bgcolor=#e7dcc3|Faces||[[triangle|{3}]][[Image:2-simplex t0.svg|25px]]
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| |bgcolor=#e7dcc3|[[Vertex figure]]||[[birectified 8-simplex]]:<BR>t<sub>2</sub>{3<sup>7</sup>} [[File:Birectified 8-simplex.png|25px]]
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| |bgcolor=#e7dcc3|[[Coxeter group]]||<math>{\tilde{E}}_8</math>, [3<sup>5,2,1</sup>]
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| |}
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| In [[geometry]], the '''1<sub>52</sub> honeycomb''' is a [[uniform tessellation]] of 8-dimensional Euclidean space. It contains '''[[Gosset 1 42 polytope|1<sub>42</sub>]]''' and '''[[demiocteract|1<sub>51</sub>]]''' [[Facet (geometry)|facets]], in a [[birectified 8-simplex]] [[vertex figure]]. It is the final figure in the [[uniform 1 k2 polytope|1<sub>k2</sub> polytope]] family.
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| ==Construction==
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| It is created by a [[Wythoff construction]] upon a set of 9 [[hyperplane]] mirrors in 8-dimensional space.
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| The facet information can be extracted from its [[Coxeter-Dynkin diagram]].
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| : {{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}} | |
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| Removing the node on the end of the 2-length branch leaves the [[8-demicube]], 1<sub>51</sub>.
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| : {{CDD|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}} | |
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| Removing the node on the end of the 5-length branch leaves the [[1 42 polytope|1<sub>42</sub>]].
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| : {{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
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| The [[vertex figure]] is determined by removing the ringed node and ringing the neighboring node. This makes the [[birectified 8-simplex]], 0<sub>52</sub>.
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| : {{CDD|nodea|3a|nodea|3a|nodea_1|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
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| {{-}}
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| == Related polytopes and honeycombs==
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| {{1 k2 polytopes}}
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| == See also ==
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| * [[5 21 honeycomb|5<sub>21</sub> honeycomb]]
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| * [[2 51 honeycomb|2<sub>51</sub> honeycomb]]
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| ==References==
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| * [[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)
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| * [[Harold Scott MacDonald Coxeter|Coxeter]] ''Regular Polytopes'' (1963), Macmillian Company
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| ** ''Regular Polytopes'', Third edition, (1973), Dover edition, ISBN 0-486-61480-8 (Chapter 5: The Kaleidoscope)
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| * '''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] [http://books.google.com/books?id=fUm5Mwfx8rAC&lpg=PP1&dq=Coxeter&pg=PP1#v=onepage&q&f=false GoogleBook]
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| ** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
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| {{Honeycombs}}
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| [[Category:9-polytopes]]
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I'm Woodrow (25) from Restoule, Canada.
I'm learning French literature at a local high school and I'm just about to graduate.
I have a part time job in a university.
Here is my web blog: want talk psychic