Pentiruncitruncated 6-simplex: Difference between revisions
Content deleted Content added
cd |
|||
| Line 8: | Line 8: | ||
|bgcolor=#e7dcc3|[[Schläfli symbol]]|| t<sub>0,1,3,5</sub>{3,3,3,3,3} |
|bgcolor=#e7dcc3|[[Schläfli symbol]]|| t<sub>0,1,3,5</sub>{3,3,3,3,3} |
||
|- |
|- |
||
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]s||{{CDD|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}} |
|||
|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]] |
|||
|- |
|- |
||
|bgcolor=#e7dcc3|5-faces||126 |
|bgcolor=#e7dcc3|5-faces||126 |
||
Revision as of 00:05, 18 April 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".
 | This geometry-related article is a stub. You can help Wikipedia by expanding it. |