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Cantellated 8-simplexes
From Wikipedia, the free encyclopedia
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In eight-dimensional geometry, a cantellated 8-simplex is a convex uniform 8-polytope, being a cantellation of the regular 8-simplex.
There are six unique cantellations for the 8-simplex, including permutations of truncation.
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Cantellated 8-simplex
Cantellated 8-simplex | |
---|---|
Type | uniform 8-polytope |
Schläfli symbol | rr{3,3,3,3,3,3,3} |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7-faces | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 1764 |
Vertices | 252 |
Vertex figure | 6-simplex prism |
Coxeter group | A8, [37], order 362880 |
Properties | convex |
Alternate names
- Small rhombated enneazetton (acronym: srene) (Jonathan Bowers)[1]
Coordinates
The Cartesian coordinates of the vertices of the cantellated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,1,1,2). This construction is based on facets of the cantellated 9-orthoplex.
Images
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Bicantellated 8-simplex
Alternate names
- Small birhombated enneazetton (acronym: sabrene) (Jonathan Bowers)[2]
Coordinates
The Cartesian coordinates of the vertices of the bicantellated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,1,2,2). This construction is based on facets of the bicantellated 9-orthoplex.
Images
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Tricantellated 8-simplex
Alternate names
- Small trirhombihexadecaexon (acronym: satrene) (Jonathan Bowers)[3]
Coordinates
The Cartesian coordinates of the vertices of the tricantellated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,1,2,2). This construction is based on facets of the tricantellated 9-orthoplex.
Images
Cantitruncated 8-simplex
Alternate names
- Great rhombated enneazetton (acronym: grene) (Jonathan Bowers)[4]
Coordinates
The Cartesian coordinates of the vertices of the cantitruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,1,2,3). This construction is based on facets of the bicantitruncated 9-orthoplex.
Images
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Bicantitruncated 8-simplex
Alternate names
- Great birhombated enneazetton (acronym: gabrene) (Jonathan Bowers)[5]
Coordinates
The Cartesian coordinates of the vertices of the bicantitruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,2,3,3). This construction is based on facets of the bicantitruncated 9-orthoplex.
Images
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Tricantitruncated 8-simplex
- Great trirhombated enneazetton (acronym: gatrene) (Jonathan Bowers)[6]
Coordinates
The Cartesian coordinates of the vertices of the tricantitruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,2,3,3,3). This construction is based on facets of the bicantitruncated 9-orthoplex.
Images
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Related polytopes
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.
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Notes
References
External links
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