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| | Lashonda Piercy is the name [http://www.Wonderhowto.com/search/persons/ persons] use to connect with me and I appreciate it. The detail [http://Photo.net/gallery/tag-search/search?query_string=I+adore I adore] most bee trying to keep but I wrestle to come across time for it. My family lives in District of Columbia but I will have to shift in a 12 months or two. Details processing is my career. See what is new on my site listed here: http://louisianastrawberries.net/ActivityFeed/MyProfile/tabid/61/UserId/553189/Default.aspx<br><br>Look at my webpage :: [http://louisianastrawberries.net/ActivityFeed/MyProfile/tabid/61/UserId/553189/Default.aspx air max mujer baratas] |
| !bgcolor=#e7dcc3 colspan=2|Omnitruncated 5-simplex honeycomb
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| |bgcolor=#ffffff align=center colspan=2|(No image)
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| |bgcolor=#e7dcc3|Type||[[Uniform_6-polytope#Regular_and_uniform_honeycombs|Uniform honeycomb]]
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| |bgcolor=#e7dcc3|Family||[[Omnitruncated simplectic honeycomb]]
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| |bgcolor=#e7dcc3|[[Schläfli symbol]]||t<sub>012345</sub>{3<sup>[6]</sup>}
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| |bgcolor=#e7dcc3|[[Coxeter–Dynkin diagram]]||{{CDD|node_1|split1|nodes_11|3ab|nodes_11|split2|node_1}}
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| |bgcolor=#e7dcc3|5-face types||[[Omnitruncated 5-simplex|t<sub>01234</sub>{3,3,3,3}]] [[File:5-simplex t01234.svg|40px]]
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| |bgcolor=#e7dcc3|4-face types||[[Omnitruncated 5-cell|t<sub>0123</sub>{3,3,3}]][[Image:Schlegel half-solid omnitruncated 5-cell.png|25px]]<BR>[[Truncated octahedral prism|{}×t<sub>012</sub>{3,3}]][[Image:Truncated octahedral prism.png|25px]]<BR>[[Duoprism|{6}×{6}]][[Image:6-6 duoprism.png|25px]]
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| |bgcolor=#e7dcc3|Cell types||[[truncated octahedron|t<sub>012</sub>{3,3}]][[Image:Truncated octahedron.png|25px]]<BR>[[cube|{4,3}]][[Image:Tetragonal prism.png|25px]]<BR>[[hexagonal prism|{}x{6}]][[Image:Hexagonal prism.png|25px]]
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| |bgcolor=#e7dcc3|Face types||[[Square|{4}]]<BR>[[Hexagon|{6}]]
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| |bgcolor=#e7dcc3|Vertex figure||[[File:Omnitruncated 5-simplex honeycomb verf.png|62px]]<BR>Irr. [[5-simplex]]
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| |bgcolor=#e7dcc3|[[Coxeter notation|Symmetry]]||<math>{\tilde{A}}_5</math>×12, [6[3<sup>[6]</sup>]]
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| |bgcolor=#e7dcc3|Properties||[[vertex-transitive]]
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| |}
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| In [[Five-dimensional space|five-dimensional]] [[Euclidean geometry]], the '''omnitruncated 5-simplex honeycomb''' or '''omnitruncated hexateric honeycomb''' is a space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]). It is composed entirely of [[omnitruncated 5-simplex]] facets.
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| The facets of all [[omnitruncated simplectic honeycomb]]s are called [[permutahedron|permutahedra]] and can be positioned in ''n+1'' space with integral coordinates, permutations of the whole numbers (0,1,..,n).
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| == A<sub>5</sub><sup>*</sup> lattice ==
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| The A{{sup sub|*|5}} lattice (also called A{{sup sub|6|5}}) is the union of six [[A5 lattice|A<sub>5</sub> lattices]], and is the dual [[vertex arrangement]] to the ''omnitruncated 5-simplex honeycomb'', and therefore the [[Voronoi cell]] of this lattice is an [[omnitruncated 5-simplex]].
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| :
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| {{CDD|node_1|split1|nodes|3ab|nodes|split2|node}} +
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| {{CDD|node|split1|nodes_10lr|3ab|nodes|split2|node}} +
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| {{CDD|node|split1|nodes_01lr|3ab|nodes|split2|node}} +
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| {{CDD|node|split1|nodes|3ab|nodes_10lr|split2|node}} +
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| {{CDD|node|split1|nodes|3ab|nodes_01lr|split2|node}} +
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| {{CDD|node|split1|nodes|3ab|nodes|split2|node_1}} = dual of {{CDD|node_1|split1|nodes_11|3ab|nodes_11|split2|node_1}}
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| == Related polytopes and honeycombs ==
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| {{5-simplex honeycomb family}}
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| === Projection by folding ===
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| The ''omnitruncated 5-simplex honeycomb'' can be projected into the 3-dimensional [[omnitruncated cubic honeycomb]] by a [[Coxeter–Dynkin diagram#Geometric folding|geometric folding]] operation that maps two pairs of mirrors into each other, sharing the same 3-space [[vertex arrangement]]:
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| {|class=wikitable
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| !<math>{\tilde{A}}_5</math>
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| |{{CDD|node_1|split1|nodes_11|3ab|nodes_11|split2|node_1}}
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| !<math>{\tilde{C}}_3</math>
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| |{{CDD|node_1|4|node_1|3|node_1|4|node_1}}
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| |}
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| ==See also==
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| Regular and uniform honeycombs in 5-space:
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| *[[5-cube honeycomb]]
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| *[[5-demicube honeycomb]]
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| *[[5-simplex honeycomb]]
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| ==Notes==
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| {{reflist}}
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| == References ==
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| * [[Norman Johnson (mathematician)|Norman Johnson]] ''Uniform Polytopes'', Manuscript (1991)
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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]
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| ** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings)
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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:Honeycombs (geometry)]]
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| [[Category:6-polytopes]]
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Lashonda Piercy is the name persons use to connect with me and I appreciate it. The detail I adore most bee trying to keep but I wrestle to come across time for it. My family lives in District of Columbia but I will have to shift in a 12 months or two. Details processing is my career. See what is new on my site listed here: http://louisianastrawberries.net/ActivityFeed/MyProfile/tabid/61/UserId/553189/Default.aspx
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