Rectified 9-cubes
 9-orthoplex    
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 Rectified 9-orthoplex
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 Birectified 9-orthoplex
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 Trirectified 9-orthoplex
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 Quadrirectified 9-cube
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 Trirectified 9-cube
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 Birectified 9-cube
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 Rectified 9-cube
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 9-cube
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| Orthogonal projections in BC9 Coxeter plane | |||
|---|---|---|---|
In nine-dimensional geometry, a rectified 9-cube is a convex uniform 9-polytope, being a rectification of the regular 9-cube.
There are 9 rectifications of the 9-cube. The zeroth is the 9-cube itself, and the 8th is the dual 9-orthoplex. Vertices of the rectified 9-cube are located at the edge-centers of the 9-orthoplex. Vertices of the birectified 9-cube are located in the square face centers of the 9-cube. Vertices of the trirectified 9-orthoplex are located in the cube cell centers of the 9-cube. Vertices of the quadrirectified 9-cube are located in the tesseract centers of the 9-cube.
These polytopes are part of a family 511 uniform 9-polytopes with BC9 symmetry.
Rectified 9-cube
[edit]Alternate names
[edit]- Rectified enneract (Acronym ren) (Jonathan Bowers)[1]
Images
[edit]| B9 | B8 | B7 | |||
|---|---|---|---|---|---|
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| [18] | [16] | [14] | |||
| B6 | B5 | ||||
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| [12] | [10] | ||||
| B4 | B3 | B2 | |||
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| [8] | [6] | [4] | |||
| A7 | A5 | A3 | |||
| — | — | — | |||
| [8] | [6] | [4] | |||
Birectified 9-cube
[edit]Alternate names
[edit]- Birectified enneract (Acronym barn) (Jonathan Bowers)[2]
Images
[edit]| B9 | B8 | B7 | |||
|---|---|---|---|---|---|
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| [18] | [16] | [14] | |||
| B6 | B5 | ||||
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| [12] | [10] | ||||
| B4 | B3 | B2 | |||
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| [8] | [6] | [4] | |||
| A7 | A5 | A3 | |||
| — | — | — | |||
| [8] | [6] | [4] | |||
Trirectified 9-cube
[edit]Alternate names
[edit]- Trirectified enneract (Acronym tarn) (Jonathan Bowers)[3]
Images
[edit]| B9 | B8 | B7 | |||
|---|---|---|---|---|---|
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| [18] | [16] | [14] | |||
| B6 | B5 | ||||
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| [12] | [10] | ||||
| B4 | B3 | B2 | |||
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| [8] | [6] | [4] | |||
| A7 | A5 | A3 | |||
| — | — | — | |||
| [8] | [6] | [4] | |||
Quadrirectified 9-cube
[edit]Alternate names
[edit]- Quadrirectified enneract (Acronym nav) (Jonathan Bowers)[4]
Images
[edit]| B9 | B8 | B7 | |||
|---|---|---|---|---|---|
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| [18] | [16] | [14] | |||
| B6 | B5 | ||||
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| [12] | [10] | ||||
| B4 | B3 | B2 | |||
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| [8] | [6] | [4] | |||
| A7 | A5 | A3 | |||
| — | — | — | |||
| [8] | [6] | [4] | |||
Notes
[edit]References
[edit]- H.S.M. Coxeter:
- H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
- Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
- (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
- (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
- Norman Johnson Uniform Polytopes, Manuscript (1991)
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966)
- Klitzing, Richard. "9D uniform polytopes (polyyotta)". x3o3o3o3o3o3o3o4o - vee, o3x3o3o3o3o3o3o4o - riv, o3o3x3o3o3o3o3o4o - brav, o3o3o3x3o3o3o3o4o - tarv, o3o3o3o3x3o3o3o4o - nav, o3o3o3o3o3x3o3o4o - tarn, o3o3o3o3o3o3x3o4o - barn, o3o3o3o3o3o3o3x4o - ren, o3o3o3o3o3o3o3o4x - enne