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| !bgcolor=#e7dcc3 colspan=2|quarter cubic honeycomb
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| |bgcolor=#ffffff align=center colspan=2|(No image)
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| |bgcolor=#e7dcc3|Type||[[Uniform_polyteron#Regular_and_uniform_honeycombs|Uniform 4-honeycomb]]
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| |bgcolor=#e7dcc3|Family||[[Quarter hypercubic honeycomb]]
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| |bgcolor=#e7dcc3|[[Schläfli symbol]]||t<sub>1</sub>{4,3,3,4}<BR>t<sub>1</sub>{4,3<sup>1,1</sup>}<BR>t<sub>3</sub>{4,3<sup>1,1</sup>}<BR>q{4,3,3,4}
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| |bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]||
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| {{CDD|node|4|node_1|3|node|3|node|4|node}}<BR>
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| {{CDD|node|4|node_1|3|node|split1|nodes}}<BR>
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| {{CDD|nodes_11|split2|node|3|node|4|node}}<BR>
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| {{CDD|nodes_10ru|split2|node|split1|nodes_10lu}} = {{CDD|node_h1|4|node|3|node|3|node|4|node_h1}}
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| |bgcolor=#e7dcc3|4-face type||[[16-cell|h{4,3<sup>2</sup>}]],[[File:Schlegel_wireframe_16-cell.png|40px]]<BR>[[Rectified tesseract|h<sub>3</sub>{4,3<sup>2</sup>}]], [[File:Schlegel_half-solid_rectified_8-cell.png|40px]]
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| |bgcolor=#e7dcc3|Cell type||[[tetrahedron|{3,3}]], [[File:Tetrahedron.png|20px]]<BR>[[Cuboctahedron|t<sub>1</sub>{4,3}]], [[File:Cuboctahedron.png|20px]]
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| |bgcolor=#e7dcc3|Face type||[[Triangle|{3}]]<BR>[[Square|{4}]]
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| |bgcolor=#e7dcc3|[[Edge figure]]||[[File:Square pyramid.png|40px]]<BR>[[Square pyramid]]
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| |bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Rectified_tesseractic_honeycomb_verf.png|80px]]<BR>Elongated [[octahedral prism|{3,4}×{}]]
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| |bgcolor=#e7dcc3|[[Coxeter group]]||<math>{\tilde{C}}_4</math> = [4,3,3,4]<BR><math>{\tilde{B}}_4</math> = [4,3<sup>1,1</sup>]<BR><math>{\tilde{D}}_4</math> = [3<sup>1,1,1,1</sup>]
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| |bgcolor=#e7dcc3|Dual||
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| |bgcolor=#e7dcc3|Properties||[[vertex-transitive]]
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| |}
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| In [[Four-dimensional space|four-dimensional]] [[Euclidean geometry]], the '''rectified tesseractic honeycomb''' is a uniform space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) in Euclidean 4-space. It is constructed by a [[rectification (geometry)|rectification]] of a [[tesseractic honeycomb]] which creates new vertices on the middle of all the original edges, rectifying the cells into [[rectified tesseract]]s, and adding new [[16-cell]] facets at the original vertices. Its [[vertex figure]] is an [[octahedral prism]], {3,4}×{}.
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| It is also called a '''quarter tesseractic honeycomb''' since it has half the vertices of the [[4-demicubic honeycomb]], and a quarter of the vertices of a [[tesseractic honeycomb]].<ref>Coxeter, '''Regular and Semi-Regular Polytopes III''', (1988), p318</ref>
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| <!--==Coordinates==
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| Vertices can be placed at all [[integer]] coordinates (i,j,k,l), such that (i+j+k+l) [[modulo]] 4=0.-->
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| == Related honeycombs==
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| {{C4_honeycombs}}
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| {{B4_honeycombs}}
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| {{D4_honeycombs}}
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| == See also ==
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| Regular and uniform honeycombs in 4-space:
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| *[[Tesseractic honeycomb]]
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| *[[Demitesseractic honeycomb]]
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| *[[24-cell honeycomb]]
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| *[[Truncated 24-cell honeycomb]]
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| *[[Snub 24-cell honeycomb]]
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| * [[5-cell honeycomb]]
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| * [[Truncated 5-cell honeycomb]]
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| * [[Omnitruncated 5-cell honeycomb]]
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| ==Notes==
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| {{reflist}}
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| == References ==
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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 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45] See p318 [http://books.google.com/books?id=fUm5Mwfx8rAC&lpg=PA318&ots=dnT1LYgmij&dq=%22quarter%20cubic%20honeycomb%22%20q%7B4%2C3%2C4%7D&pg=PA318#v=onepage&q=%22quarter%20cubic%20honeycomb%22%20q%7B4,3,4%7D&f=false]
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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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| * {{KlitzingPolytopes|flat.htm|4D|Euclidean tesselations#4D}} o4x3o3o4o, o3o3o *b3x4o, x3o3x *b3o4o, x3o3x *b3o *b3o - rittit - O87
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| * {{cite book |author=Conway JH, Sloane NJH |year=1998 |title=Sphere Packings, Lattices and Groups |edition=3rd |isbn=0-387-98585-9}}
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| {{Honeycombs}}
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| {{DEFAULTSORT:Demitesseractic Honeycomb}}
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| [[Category:Honeycombs (geometry)]]
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| [[Category:5-polytopes]]
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