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| | I am Kimberly from Cannes. I love to play Clarinet. Other hobbies are Australian Football League. |
| !bgcolor=#e7dcc3 colspan=2|Omnitruncated 4-simplex 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||[[Omnitruncated simplectic honeycomb]]
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| |bgcolor=#e7dcc3|[[Schläfli symbol]]||t<sub>0,1,2,3,4</sub>{3<sup>[5]</sup>}
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| |bgcolor=#e7dcc3|[[Coxeter diagram]]||{{CDD|node_1|split1|nodes_11|3ab|branch_11}}
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| |bgcolor=#e7dcc3|4-face types||[[Omnitruncated 5-cell|t<sub>0,1,2,3</sub>{3,3,3}]] [[File:Schlegel half-solid omnitruncated 5-cell.png|40px]]
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| |bgcolor=#e7dcc3|Cell types||[[Truncated octahedron|t<sub>0,1,2</sub>{3,3}]] [[File:Uniform polyhedron-33-t012.png|20px]]<BR>[[Hexagonal prism|{6}x{}]] [[File:Hexagonal prism.png|20px]]
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| |bgcolor=#e7dcc3|Face types||[[Square (geometry)|{4}]]<BR>[[Hexagon|{6}]]
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| |bgcolor=#e7dcc3|Vertex figure||[[File:Omnitruncated 4-simplex honeycomb verf.png|80px]]<BR>Irr. [[5-cell]]
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| |bgcolor=#e7dcc3|[[Coxeter notation|Symmetry]]||<math>{\tilde{A}}_4</math>×10, <nowiki>[5[</nowiki>3<sup>[5]</sup>]]
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| |bgcolor=#e7dcc3|Properties||[[vertex-transitive]], [[cell-transitive]]
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| In [[Four-dimensional space|four-dimensional]] [[Euclidean geometry]], the '''omnitruncated 4-simplex honeycomb''' or '''omnitruncated 5-cell honeycomb''' is a space-filling [[tessellation]] [[honeycomb (geometry)|honeycomb]]. It is composed entirely of [[omnitruncated 5-cell]] (omnitruncated 4-simplex) facets.
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| [[Coxeter]] calls this '''Hinton's honeycomb''' after [[Charles Howard Hinton|C. H. Hinton]], who described it in his book ''The Fourth Dimension'' in 1906.<ref name=cox>{{cite book|title=The Beauty of Geometry: Twelve Essays|year= 1999|publisher= Dover Publications|lccn=99035678|isbn= 0-486-40919-8 }} (The classification of Zonohededra, page 73)</ref>
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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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| == Alernate names==
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| * Omnitruncated cyclopentachoric tetracomb
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| * Great-prismatodecachoric tetracomb
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| == A<sub>4</sub><sup>*</sup> lattice ==
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| The A{{sup sub|*|4}} lattice is the union of five A<sub>4</sub> lattices, and is the dual to the [[omnitruncated 5-simplex honeycomb]], and therefore the [[Voronoi cell]] of this lattice is an [[omnitruncated 5-cell]]
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| : {{CDD|node_1|split1|nodes|3ab|branch}} + {{CDD|node|split1|nodes_10lur|3ab|branch}} + {{CDD|node|split1|nodes_01lr|3ab|branch}} + {{CDD|node|split1|nodes|3ab|branch_10l}} + {{CDD|node|split1|nodes|3ab|branch_01l}} = dual of {{CDD|node_1|split1|nodes_11|3ab|branch_11}}
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| == Related polytopes and honeycombs ==
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| {{4-simplex_honeycomb_family}}
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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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| *[[16-cell 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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| ==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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| * {{Cite book|title=Kaleidoscopes: Selected Writings of H.S.M. Coxeter|editor= F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss|publisher=Wiley-Interscience Publication|year= 1995|isbn=978-0-471-01003-6|url=http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html}}
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| ** (Paper 22) {{Cite journal|doi=10.1007/BF01181449|title=Regular and semi-regular polytopes. I|year=1940|last1=Coxeter|first1=H. S. M.|journal=Mathematische Zeitschrift|volume=46|pages=380}} (1.9 Uniform space-fillings)
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| ** (Paper 24) {{Cite journal|doi=10.1007/BF01161745|title=Regular and semi-regular polytopes. III|year=1988|last1=Coxeter|first1=H. S. M.|journal=Mathematische Zeitschrift|volume=200|pages=3}}
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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)'' Model 140
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| * {{KlitzingPolytopes|flat.htm|4D|Euclidean tesselations}}, x3x3x3x3x3*a - otcypit - 140
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| {{Honeycombs}}
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| [[Category:Honeycombs (geometry)]]
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| [[Category:5-polytopes]]
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I am Kimberly from Cannes. I love to play Clarinet. Other hobbies are Australian Football League.