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Rectified 10-simplexes
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In ten-dimensional geometry, a rectified 10-simplex is a convex uniform 10-polytope, being a rectification of the regular 10-simplex.
These polytopes are part of a family of 527 uniform 10-polytopes with A10 symmetry.
There are unique 5 degrees of rectifications including the zeroth, the 10-simplex itself. Vertices of the rectified 10-simplex are located at the edge-centers of the 10-simplex. Vertices of the birectified 10-simplex are located in the triangular face centers of the 10-simplex. Vertices of the trirectified 10-simplex are located in the tetrahedral cell centers of the 10-simplex. Vertices of the quadrirectified 10-simplex are located in the 5-cell centers of the 10-simplex.
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Rectified 10-simplex
| Rectified 10-simplex | |
|---|---|
| Type | uniform polyxennon |
| Schläfli symbol | t1{3,3,3,3,3,3,3,3,3} |
| Coxeter-Dynkin diagrams |    |
| 9-faces | 22 |
| 8-faces | 165 |
| 7-faces | 660 |
| 6-faces | 1650 |
| 5-faces | 2772 |
| 4-faces | 3234 |
| Cells | 2640 |
| Faces | 1485 |
| Edges | 495 |
| Vertices | 55 |
| Vertex figure | 9-simplex prism |
| Petrie polygon | decagon |
| Coxeter groups | A10, [3,3,3,3,3,3,3,3,3] |
| Properties | convex |
The rectified 10-simplex is the vertex figure of the 11-demicube.
Alternate names
- Rectified hendecaxennon (Acronym ru) (Jonathan Bowers)[1]
Coordinates
The Cartesian coordinates of the vertices of the rectified 10-simplex can be most simply positioned in 11-space as permutations of (0,0,0,0,0,0,0,0,0,1,1). This construction is based on facets of the rectified 11-orthoplex.
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Birectified 10-simplex
Alternate names
- Birectified hendecaxennon (Acronym bru) (Jonathan Bowers)[2]
Coordinates
The Cartesian coordinates of the vertices of the birectified 10-simplex can be most simply positioned in 11-space as permutations of (0,0,0,0,0,0,0,0,1,1,1). This construction is based on facets of the birectified 11-orthoplex.
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Trirectified 10-simplex
Alternate names
- Trirectified hendecaxennon (Jonathan Bowers)[3]
Coordinates
The Cartesian coordinates of the vertices of the trirectified 10-simplex can be most simply positioned in 11-space as permutations of (0,0,0,0,0,0,0,1,1,1,1). This construction is based on facets of the trirectified 11-orthoplex.
Images
Quadrirectified 10-simplex
Alternate names
- Quadrirectified hendecaxennon (Acronym teru) (Jonathan Bowers)[4]
Coordinates
The Cartesian coordinates of the vertices of the quadrirectified 10-simplex can be most simply positioned in 11-space as permutations of (0,0,0,0,0,0,1,1,1,1,1). This construction is based on facets of the quadrirectified 11-orthoplex.
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Notes
References
External links
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