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Truncated 8-orthoplexes
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In eight-dimensional geometry, a truncated 8-orthoplex is a convex uniform 8-polytope, being a truncation of the regular 8-orthoplex.
There are 7 truncation for the 8-orthoplex. Vertices of the truncation 8-orthoplex are located as pairs on the edge of the 8-orthoplex. Vertices of the bitruncated 8-orthoplex are located on the triangular faces of the 8-orthoplex. Vertices of the tritruncated 7-orthoplex are located inside the tetrahedral cells of the 8-orthoplex. The final truncations are best expressed relative to the 8-cube.
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Truncated 8-orthoplex
Truncated 8-orthoplex | |
---|---|
Type | uniform 8-polytope |
Schläfli symbol | t0,1{3,3,3,3,3,3,4} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 1456 |
Vertices | 224 |
Vertex figure | ( )v{3,3,3,4} |
Coxeter groups | B8, [3,3,3,3,3,3,4] D8, [35,1,1] |
Properties | convex |
Alternate names
- Truncated octacross (acronym tek) (Jonthan Bowers)[1]
Construction
There are two Coxeter groups associated with the truncated 8-orthoplex, one with the C8 or [4,3,3,3,3,3,3] Coxeter group, and a lower symmetry with the D8 or [35,1,1] Coxeter group.
Coordinates
Cartesian coordinates for the vertices of a truncated 8-orthoplex, centered at the origin, are all 224 vertices are sign (4) and coordinate (56) permutations of
- (±2,±1,0,0,0,0,0,0)
Images
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Bitruncated 8-orthoplex
Alternate names
- Bitruncated octacross (acronym batek) (Jonthan Bowers)[2]
Coordinates
Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of
- (±2,±2,±1,0,0,0,0,0)
Images
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Tritruncated 8-orthoplex
Alternate names
- Tritruncated octacross (acronym tatek) (Jonthan Bowers)[3]
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,±1,0,0,0,0)
Images
Notes
References
External links
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