Pentiruncitruncated 6-simplex: Difference between revisions
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#REDIRECT [[Pentellated 6-simplexes#Pentiruncitruncated 6-simplex]] |
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{| class="wikitable" align="right" style="margin-left:10px" width="250" |
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!bgcolor=#e7dcc3 colspan=2|pentiruncitruncated 6-simplex |
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|bgcolor=#ffffff align=center colspan=2|[[File:6-simplex t0135.svg|280px]]<BR>A<sub>6</sub> [[Coxeter plane]] projection<BR>(7-gonal symmetry) |
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|bgcolor=#e7dcc3|Type||[[uniform polypeton]] |
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|bgcolor=#e7dcc3|[[Schläfli symbol]]|| t<sub>0,1,3,5</sub>{3,3,3,3,3} |
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|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]s||[[Image:CDW ring.png]][[Image:CDW 3b.png]][[Image:CDW ring.png]][[Image:CDW 3b.png]][[Image:CDW dot.png]][[Image:CDW 3b.png]][[Image:CDW ring.png]][[Image:CDW 3b.png]][[Image:CDW dot.png]][[Image:CDW 3b.png]][[Image:CDW ring.png]] |
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|bgcolor=#e7dcc3|5-faces||126 |
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|bgcolor=#e7dcc3|4-faces||1491 |
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|bgcolor=#e7dcc3|Cells||5565 |
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|bgcolor=#e7dcc3|Faces||8610 |
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|bgcolor=#e7dcc3|Edges||5670 |
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|bgcolor=#e7dcc3|Vertices||1260 |
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|bgcolor=#e7dcc3|[[Vertex figure]]|| |
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|bgcolor=#e7dcc3|[[Coxeter group]]s||A<sub>6</sub>, [3,3,3,3,3] |
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|bgcolor=#e7dcc3|Properties||[[Convex polytope|convex]] |
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In six-dimensional [[geometry]], a '''pentiruncitruncated 6-simplex''' is a [[uniform 6-polytope]]. |
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== Coordinates == |
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The vertices of the ''pentiruncitruncated 6-simplex'' can be most simply positioned in 7-space as permutations of (0,1,1,1,2,3,4). This construction is based on [[Facet (geometry)|facets]] of the [[pentiruncitruncated 7-orthoplex]]. |
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== Images == |
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{| class=wikitable width=480 |
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|+ [[orthogonal projection]]s in A<sub>k</sub> [[Coxeter plane]]s |
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|- align=center |
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!A<sub>5</sub> |
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!A<sub>4</sub> |
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|- align=center |
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|[[File:6-simplex t0135_A5.svg|240px]]<BR>D<sub>6</sub> symmetry |
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|[[File:6-simplex t0135_A4.svg|240px]]<BR>D<sub>5</sub> symmetry |
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|- align=center |
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!A<sub>3</sub> |
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!A<sub>2</sub> |
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|- align=center |
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|[[File:6-simplex t0135_A3.svg|240px]]<BR>D<sub>4</sub> symmetry |
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|[[File:6-simplex t0135_A2.svg|240px]]<BR>D<sub>3</sub> symmetry |
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|} |
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== Related uniform 6-polytopes == |
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This is one of 35 [[Uniform_6-polytope#The_A6_.5B3.2C3.2C3.2C3.2C3.5D_family_.286-simplex.29|uniform 6-polytopes]] based on the [3,3,3,3,3] [[Coxeter group]], all shown here in A<sub>6</sub> [[Coxeter plane]] [[orthographic projection]]s. |
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{{Heptapeton family}} |
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== See also == |
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Other [[6-polytope]]s: |
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* [[6-simplex]] - {3,3,3,3,3} |
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* [[6-orthoplex]] (hexacross) - {3,3,3,3,4} |
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* [[6-cube]] (hexeract) - {4,3,3,3,3} |
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* [[6-demicube]] (demihexeract) - {3<sup>1,3,1</sup>} |
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== Notes== |
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{{reflist}} |
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== External links == |
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*{{GlossaryForHyperspace | anchor=Cross | title=Cross polytope }} |
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* [http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions] |
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* [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary] |
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* [[Richard Klitzing]] 6D quasiregulars, (multi)prisms, non-prismatic Wythoffian polyterons [http://ogre.nu/klitzing/dimensions/polypeta.htm x3x3o3x3o3x] |
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[[Category:6-polytopes]] |
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{{Geometry-stub}} |
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