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| | Greetings! I am Marvella and I feel comfy when [http://Www.mydr.com.au/sexual-health/herpes-your-questions-answered individuals] use the full name. What I love performing is playing baseball but I haven't [http://vip.akwacity.com/oxwall/blogs/post/10278 std testing at home] made a dime with it. Since std [http://tfor.vectorsigma.ru/node/5409 home std test kit] test she was 18 she's been operating as a meter reader but she's usually wanted her [http://Www.stdtestingservice.com/how-accurate-are-at-home-std-tests/ personal business]. South Dakota is at home std testing her birth location but she needs to transfer simply because of her family.<br><br>Have a look at my web page :: [http://premium.asslikethat.com/blog/9567 http://premium.asslikethat.com/blog/9567] |
| !bgcolor=#e7dcc3 colspan=2|{{PAGENAME}} | |
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| |bgcolor=#ffffff align=center colspan=2|[[Image:Rectified cubic tiling.png|200px]][[File:HC A3-P3.png|110px]]
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| |bgcolor=#e7dcc3|Type||[[Convex uniform honeycomb|Uniform honeycomb]]
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| |bgcolor=#e7dcc3|Cells||[[Octahedron]] [[Image:Octahedron.svg|40px]]<BR>[[Cuboctahedron]] [[Image:Cuboctahedron.svg|40px]]
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| |bgcolor=#e7dcc3|[[Schläfli symbol]]||r{4,3,4}<BR>t<sub>1</sub>{4,3,4}
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| |bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]s||{{CDD|node|4|node_1|3|node|4|node}}
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| |bgcolor=#e7dcc3|Vertex figure||[[File:Rectified cubic honeycomb verf.png|80px]]<BR>[[Cuboid]]
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| |bgcolor=#e7dcc3|[[Space group]]<BR>[[Fibrifold notation]]||Pm{{overline|3}}m (221)<BR>4<sup>−</sup>:2
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| |bgcolor=#e7dcc3|[[Coxeter group]]||<math>{\tilde{C}}_3</math>, [4,3,4]
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| |bgcolor=#e7dcc3|Dual||[[oblate octahedrille]]<BR>(Square bipyramidal honeycomb)
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| |bgcolor=#e7dcc3|Properties||[[vertex-transitive]], [[edge-transitive]]
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| |}
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| The '''rectified cubic honeycomb''' is a uniform space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) in Euclidean 3-space. It is composed of [[octahedron|octahedra]] and [[cuboctahedron|cuboctahedra]] in a ratio of 1:1.
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| [[John Horton Conway]] calls this honeycomb a '''cuboctahedrille''', and its dual [[oblate octahedrille]].
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| == Symmetry ==
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| There are four [[uniform coloring]]s for the cells of this honeycomb with reflective symmetry, listed by their [[Coxeter group]], and [[Wythoff construction]] name, and the [[Coxeter-Dynkin diagram]] below.
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| {| class="wikitable" width=320
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| ![[Coxeter notation|Symmetry]]
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| ![4,3,4], <math>{\tilde{C}}_3</math><BR>=<<[3<sup>[4]</sup>]>>
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| ![4,3<sup>1,1</sup>], <math>{\tilde{B}}_3</math><BR>=<[3<sup>[4]</sup>]><sub>1</sub>
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| ![4,3<sup>1,1</sup>], <math>{\tilde{B}}_3</math><BR>=<[3<sup>[4]</sup>]><sub>2</sub>
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| ![3<sup>[4]</sup>], <math>{\tilde{A}}_3</math>
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| ![[Space group]]||Pm{{overline|3}}m<BR>(221)||Fm{{overline|3}}m<BR>(225)||Fm{{overline|3}}m<BR>(225)|| F{{overline|4}}3m<BR>(216)
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| |Coloring
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| |[[Image:Rectified cubic honeycomb.png|80px]]
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| |[[Image:Rectified cubic honeycomb4.png|80px]]
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| |[[Image:Rectified cubic honeycomb3.png|80px]]
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| |[[Image:Rectified cubic honeycomb2.png|80px]]
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| |- align=center
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| !rowspan=2|[[Coxeter-Dynkin diagram|Coxeter<BR>diagram]]
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| |{{CDD|node|4|node_1|3|node|4|node}}
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| |{{CDD|node|4|node_1|split1|nodes}}
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| |{{CDD|node|split1|nodes_11|split2|node}}
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| |- align=center
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| |{{CDD|node|4|node|3|node_1|4|node}}
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| |{{CDD|node|4|node|split1|nodes_11}}
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| |{{CDD|node_1|split1|nodes|split2|node_1}}
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| |- align=center
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| ![[Vertex figure]]
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| ||[[Image:Rectified cubic honeycomb verf.png|80px]]
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| ||[[File:Rectified alternate cubic honeycomb verf.png|80px]]
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| ||[[File:Cantellated alternate cubic honeycomb verf.png|80px]]
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| ||[[File:T02 quarter cubic honeycomb verf.png|80px]]
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| |- align=center
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| !Vertex<BR>figure<BR>symmetry
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| |[4,2]<BR>order 16
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| |[2,2]<BR>order 8
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| |[4]<BR>order 8
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| |[2]<BR>order 4
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| |}
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| == Related honeycombs==
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| The [4,3<sup>1,1</sup>], {{CDD|node|4|node|split1|nodes}}, [[Coxeter group]] generates 9 permutations of uniform tessellations, 4 with distinct geometry including the alternated cubic honeycomb.
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| {{B3 honeycombs}}
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| This honeycomb is one of [[Uniform polyteron#Regular and uniform honeycombs|five distinct uniform honeycombs]]<ref>[http://mathworld.wolfram.com/Necklace.html], [http://oeis.org/A000029 A000029] 6-1 cases, skipping one with zero marks</ref> constructed by the <math>{\tilde{A}}_3</math> [[Coxeter group]]. The symmetry can be multiplied by the symmetry of rings in the [[Coxeter–Dynkin diagram]]s: {{A3 honeycombs}}
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| == See also==
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| *[[Architectonic and catoptric tessellation]]
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| == References ==
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| {{reflist}}
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| {{Commonscat|Rectified cubic honeycomb}}
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| * [[John Horton Conway|John H. Conway]], Heidi Burgiel, Chaim Goodman-Strauss, (2008) ''The Symmetries of Things'', ISBN 978-1-56881-220-5 (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, Architectonic and Catoptric tessellations, p 292-298, includes all the nonprismatic forms)
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| * [[George Olshevsky]], ''Uniform Panoploid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)''
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| * [[Branko Grünbaum]], Uniform tilings of 3-space. [[Geombinatorics]] 4(1994), 49 - 56.
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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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| * [[Alfredo Andreini|A. Andreini]], ''Sulle reti di poliedri regolari e semiregolari e sulle corrispondenti reti correlative'' (On the regular and semiregular nets of polyhedra and on the corresponding correlative nets), Mem. Società Italiana della Scienze, Ser.3, 14 (1905) 75–129.
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| * {{KlitzingPolytopes|flat.htm|3D Euclidean Honeycombs|o4x3o4o - rich - O15}}
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| * [http://www.doskey.com/polyhedra/UniformHoneycombs.html Uniform Honeycombs in 3-Space: 02-Rich]
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| {{polychora-stub}}
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| [[Category:Honeycombs (geometry)]]
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