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Truncated 8-cubes
Convex uniform 8-polytope in 8-dimensional geometry From Wikipedia, the free encyclopedia
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In eight-dimensional geometry, a truncated 8-cube is a convex uniform 8-polytope, being a truncation of the regular 8-cube.
There are unique 7 degrees of truncation for the 8-cube. Vertices of the truncation 8-cube are located as pairs on the edge of the 8-cube. Vertices of the bitruncated 8-cube are located on the square faces of the 8-cube. Vertices of the tritruncated 7-cube are located inside the cubic cells of the 8-cube. The final truncations are best expressed relative to the 8-orthoplex.
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Truncated 8-cube
Truncated 8-cube | |
---|---|
Type | uniform 8-polytope |
Schläfli symbol | t{4,3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | ( )v{3,3,3,3,3} |
Coxeter groups | B8, [3,3,3,3,3,3,4] |
Properties | convex |
Alternate names
- Truncated octeract (acronym tocto) (Jonathan Bowers)[1]
Coordinates
Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all 224 vertices are sign (4) and coordinate (56) permutations of
- (±2,±2,±2,±2,±2,±2,±1,0)
Images
Related polytopes
The truncated 8-cube, is seventh in a sequence of truncated hypercubes:
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Bitruncated 8-cube
Alternate names
- Bitruncated octeract (acronym bato) (Jonathan Bowers)[2]
Coordinates
Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all the sign coordinate permutations of
- (±2,±2,±2,±2,±2,±1,0,0)
Images
Related polytopes
The bitruncated 8-cube is sixth in a sequence of bitruncated hypercubes:
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Tritruncated 8-cube
Alternate names
- Tritruncated octeract (acronym tato) (Jonathan Bowers)[3]
Coordinates
Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all the sign coordinate permutations of
- (±2,±2,±2,±2,±1,0,0,0)
Images
Quadritruncated 8-cube
Alternate names
- Quadritruncated octeract (acronym oke) (Jonathan Bowers)[4]
Coordinates
Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of
- (±2,±2,±2,±2,±1,0,0,0)
Images
Related polytopes
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Notes
References
External links
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