Rectified 8-cubes
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In eight-dimensional geometry, a rectified 8-cube is a convex uniform 8-polytope, being a rectification of the regular 8-cube.
![]() 8-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Rectified 8-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Birectified 8-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Trirectified 8-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Trirectified 8-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Birectified 8-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Rectified 8-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() 8-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Orthogonal projections in B8 Coxeter plane |
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There are unique 8 degrees of rectifications, the zeroth being the 8-cube, and the 7th and last being the 8-orthoplex. Vertices of the rectified 8-cube are located at the edge-centers of the 8-cube. Vertices of the birectified 8-cube are located in the square face centers of the 8-cube. Vertices of the trirectified 8-cube are located in the 7-cube cell centers of the 8-cube.
Rectified 8-cube
Rectified 8-cube | |
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Type | uniform 8-polytope |
Schläfli symbol | t1{4,3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7-faces | 256 + 16 |
6-faces | 2048 + 112 |
5-faces | 7168 + 448 |
4-faces | 14336 + 1120 |
Cells | 17920 +* 1792 |
Faces | 4336 + 1792 |
Edges | 7168 |
Vertices | 1024 |
Vertex figure | 6-simplex prism {3,3,3,3,3}×{} |
Coxeter groups | B8, [36,4] D8, [35,1,1] |
Properties | convex |
Alternate names
- rectified octeract
Images
B8 | B7 | ||||
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[16] | [14] | ||||
B6 | B5 | ||||
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[12] | [10] | ||||
B4 | B3 | B2 | |||
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[8] | [6] | [4] | |||
A7 | A5 | A3 | |||
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[8] | [6] | [4] |
Birectified 8-cube
Birectified 8-cube | |
---|---|
Type | uniform 8-polytope |
Coxeter symbol | 0511 |
Schläfli symbol | t2{4,3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7-faces | 256 + 16 |
6-faces | 1024 + 2048 + 112 |
5-faces | 7168 + 7168 + 448 |
4-faces | 21504 + 14336 + 1120 |
Cells | 35840 + 17920 + 1792 |
Faces | 35840 + 14336 |
Edges | 21504 |
Vertices | 1792 |
Vertex figure | {3,3,3,3}x{4} |
Coxeter groups | B8, [36,4] D8, [35,1,1] |
Properties | convex |
Alternate names
- Birectified octeract
- Rectified 8-demicube
Images
B8 | B7 | ||||
---|---|---|---|---|---|
![]() |
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[16] | [14] | ||||
B6 | B5 | ||||
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[12] | [10] | ||||
B4 | B3 | B2 | |||
![]() |
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[8] | [6] | [4] | |||
A7 | A5 | A3 | |||
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[8] | [6] | [4] |
Trirectified 8-cube
Triectified 8-cube | |
---|---|
Type | uniform 8-polytope |
Schläfli symbol | t3{4,3,3,3,3,3,3} |
Coxeter diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7-faces | 16+256 |
6-faces | 1024 + 2048 + 112 |
5-faces | 1792 + 7168 + 7168 + 448 |
4-faces | 1792 + 10752 + 21504 +14336 |
Cells | 8960 + 26880 + 35840 |
Faces | 17920+35840 |
Edges | 17920 |
Vertices | 1152 |
Vertex figure | {3,3,3}x{3,4} |
Coxeter groups | B8, [36,4] D8, [35,1,1] |
Properties | convex |
Alternate names
- trirectified octeract
Images
B8 | B7 | ||||
---|---|---|---|---|---|
![]() |
![]() | ||||
[16] | [14] | ||||
B6 | B5 | ||||
![]() |
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[12] | [10] | ||||
B4 | B3 | B2 | |||
![]() |
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[8] | [6] | [4] | |||
A7 | A5 | A3 | |||
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[8] | [6] | [4] |
Notes
References
External links
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