Truncated 7-simplexes

Uniform 7-polytope From Wikipedia, the free encyclopedia

Truncated 7-simplexes

In seven-dimensional geometry, a truncated 7-simplex is a convex uniform 7-polytope, being a truncation of the regular 7-simplex.

More information Orthogonal projections in A7 Coxeter plane ...
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7-simplex
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Truncated 7-simplex
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Bitruncated 7-simplex
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Tritruncated 7-simplex
Orthogonal projections in A7 Coxeter plane
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There are unique 3 degrees of truncation. Vertices of the truncation 7-simplex are located as pairs on the edge of the 7-simplex. Vertices of the bitruncated 7-simplex are located on the triangular faces of the 7-simplex. Vertices of the tritruncated 7-simplex are located inside the tetrahedral cells of the 7-simplex.

Truncated 7-simplex

Truncated 7-simplex
Typeuniform 7-polytope
Schläfli symbolt{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces16
5-faces
4-faces
Cells350
Faces336
Edges196
Vertices56
Vertex figure( )v{3,3,3,3}
Coxeter groupsA7, [3,3,3,3,3,3]
Propertiesconvex, Vertex-transitive

In seven-dimensional geometry, a truncated 7-simplex is a convex uniform 7-polytope, being a truncation of the regular 7-simplex.

Alternate names

  • Truncated octaexon (Acronym: toc) (Jonathan Bowers)[1]

Coordinates

The vertices of the truncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,0,1,2). This construction is based on facets of the truncated 8-orthoplex.

Images

More information Ak Coxeter plane, A7 ...
orthographic projections
Ak Coxeter plane A7 A6 A5
Graph Thumb Thumb Thumb
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph Thumb Thumb Thumb
Dihedral symmetry [5] [4] [3]
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Bitruncated 7-simplex

More information Bitruncated 7-simplex ...
Bitruncated 7-simplex
Typeuniform 7-polytope
Schläfli symbol2t{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges588
Vertices168
Vertex figure{ }v{3,3,3}
Coxeter groupsA7, [3,3,3,3,3,3]
Propertiesconvex, Vertex-transitive
Close

Alternate names

  • Bitruncated octaexon (acronym: bittoc) (Jonathan Bowers)[2]

Coordinates

The vertices of the bitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,1,2,2). This construction is based on facets of the bitruncated 8-orthoplex.

Images

More information Ak Coxeter plane, A7 ...
orthographic projections
Ak Coxeter plane A7 A6 A5
Graph Thumb Thumb Thumb
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph Thumb Thumb Thumb
Dihedral symmetry [5] [4] [3]
Close

Tritruncated 7-simplex

More information Tritruncated 7-simplex ...
Tritruncated 7-simplex
Typeuniform 7-polytope
Schläfli symbol3t{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges980
Vertices280
Vertex figure{3}v{3,3}
Coxeter groupsA7, [3,3,3,3,3,3]
Propertiesconvex, Vertex-transitive
Close

Alternate names

  • Tritruncated octaexon (acronym: tattoc) (Jonathan Bowers)[3]

Coordinates

The vertices of the tritruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,2,2,2). This construction is based on facets of the tritruncated 8-orthoplex.

Images

More information Ak Coxeter plane, A7 ...
orthographic projections
Ak Coxeter plane A7 A6 A5
Graph Thumb Thumb Thumb
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph Thumb Thumb Thumb
Dihedral symmetry [5] [4] [3]
Close

These three polytopes are from a set of 71 uniform 7-polytopes with A7 symmetry.

See also

Notes

References

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