Rectified 8-cubes

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Rectified 8-cubes

In eight-dimensional geometry, a rectified 8-cube is a convex uniform 8-polytope, being a rectification of the regular 8-cube.

More information 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
Typeuniform 8-polytope
Schläfli symbolt1{4,3,3,3,3,3,3}
Coxeter-Dynkin diagrams
7-faces256 + 16
6-faces2048 + 112
5-faces7168 + 448
4-faces14336 + 1120
Cells17920 +* 1792
Faces4336 + 1792
Edges7168
Vertices1024
Vertex figure6-simplex prism
{3,3,3,3,3}×{}
Coxeter groupsB8, [36,4]
D8, [35,1,1]
Propertiesconvex

Alternate names

  • rectified octeract

Images

More information B8, B7 ...
orthographic projections
B8 B7
Thumb Thumb
[16] [14]
B6 B5
Thumb Thumb
[12] [10]
B4 B3 B2
Thumb Thumb Thumb
[8] [6] [4]
A7 A5 A3
Thumb Thumb Thumb
[8] [6] [4]
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Birectified 8-cube

More information Birectified 8-cube ...
Birectified 8-cube
Typeuniform 8-polytope
Coxeter symbol0511
Schläfli symbolt2{4,3,3,3,3,3,3}
Coxeter-Dynkin diagrams
7-faces256 + 16
6-faces1024 + 2048 + 112
5-faces7168 + 7168 + 448
4-faces21504 + 14336 + 1120
Cells35840 + 17920 + 1792
Faces35840 + 14336
Edges21504
Vertices1792
Vertex figure{3,3,3,3}x{4}
Coxeter groupsB8, [36,4]
D8, [35,1,1]
Propertiesconvex
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Alternate names

  • Birectified octeract
  • Rectified 8-demicube

Images

More information B8, B7 ...
orthographic projections
B8 B7
Thumb Thumb
[16] [14]
B6 B5
Thumb Thumb
[12] [10]
B4 B3 B2
Thumb Thumb Thumb
[8] [6] [4]
A7 A5 A3
Thumb Thumb Thumb
[8] [6] [4]
Close

Trirectified 8-cube

More information Triectified 8-cube ...
Triectified 8-cube
Typeuniform 8-polytope
Schläfli symbolt3{4,3,3,3,3,3,3}
Coxeter diagrams
7-faces16+256
6-faces1024 + 2048 + 112
5-faces1792 + 7168 + 7168 + 448
4-faces1792 + 10752 + 21504 +14336
Cells8960 + 26880 + 35840
Faces17920+35840
Edges17920
Vertices1152
Vertex figure{3,3,3}x{3,4}
Coxeter groupsB8, [36,4]
D8, [35,1,1]
Propertiesconvex
Close

Alternate names

  • trirectified octeract

Images

More information B8, B7 ...
orthographic projections
B8 B7
Thumb Thumb
[16] [14]
B6 B5
Thumb Thumb
[12] [10]
B4 B3 B2
Thumb Thumb Thumb
[8] [6] [4]
A7 A5 A3
Thumb Thumb Thumb
[8] [6] [4]
Close

Notes

References

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