Pentiruncitruncated 6-simplex: Difference between revisions
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* [http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions] |
* [http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions] |
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* [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary] |
* [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary] |
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* {{KlitzingPolytopes|polypeta.htm|6D uniform polytopes (polypeta)|x3x3o3x3o3x - tocral}} |
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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]] |
[[Category:6-polytopes]] |
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Revision as of 22:05, 31 March 2011
| pentiruncitruncated 6-simplex | |
|---|---|
 A6 Coxeter plane projection (7-gonal symmetry) | |
| Type | uniform polypeton |
| Schläfli symbol | t0,1,3,5{3,3,3,3,3} |
| Coxeter-Dynkin diagrams |   
|
| 5-faces | 126 |
| 4-faces | 1491 |
| Cells | 5565 |
| Faces | 8610 |
| Edges | 5670 |
| Vertices | 1260 |
| Vertex figure | |
| Coxeter groups | A6, [3,3,3,3,3] |
| Properties | convex |
In six-dimensional geometry, a pentiruncitruncated 6-simplex is a uniform 6-polytope.
Alternate names
- Tericellirhombated heptapeton (Acronym: tocral) (Jonathan Bowers)
Coordinates
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 facets of the pentiruncitruncated 7-orthoplex.
Images
| Ak Coxeter plane | A6 | A5 | A4 |
|---|---|---|---|
| Graph |
|
|
|
| Dihedral symmetry | [7] | [6] | [5] |
| Ak Coxeter plane | A3 | A2 | |
| Graph | 
|
| |
| Dihedral symmetry | [4] | [3] |
Related uniform 6-polytopes
This is one of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown here in A6 Coxeter plane orthographic projections.
See also
Other 6-polytopes:
- 6-simplex - {3,3,3,3,3}
- 6-orthoplex (hexacross) - {3,3,3,3,4}
- 6-cube (hexeract) - {4,3,3,3,3}
- 6-demicube (demihexeract) - {31,3,1}
Notes
External links
- Olshevsky, George. "Cross polytope". Glossary for Hyperspace. Archived from the original on 4 February 2007.
- Polytopes of Various Dimensions
- Multi-dimensional Glossary
- Klitzing, Richard. "6D uniform polytopes (polypeta) x3x3o3x3o3x - tocral".
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