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Cantellated 8-simplexes

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Cantellated 8-simplexes
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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.

More information Orthogonal projections in A8 Coxeter plane ...

There are six unique cantellations for the 8-simplex, including permutations of truncation.

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Cantellated 8-simplex

Cantellated 8-simplex
Typeuniform 8-polytope
Schläfli symbolrr{3,3,3,3,3,3,3}
Coxeter-Dynkin diagram
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges1764
Vertices252
Vertex figure6-simplex prism
Coxeter groupA8, [37], order 362880
Propertiesconvex

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

More information Ak Coxeter plane, A8 ...
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Bicantellated 8-simplex

More information 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

More information Ak Coxeter plane, A8 ...
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Tricantellated 8-simplex

More information 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

More information Ak Coxeter plane, A8 ...

Cantitruncated 8-simplex

More information 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

More information Ak Coxeter plane, A8 ...
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Bicantitruncated 8-simplex

More information 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

More information Ak Coxeter plane, A8 ...
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Tricantitruncated 8-simplex

More information 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

More information Ak Coxeter plane, A8 ...
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This polytope is one of 135 uniform 8-polytopes with A8 symmetry.

More information A8 polytopes ...
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Notes

References

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