Truncated 7-simplexes


7-simplex

Truncated 7-simplex

Bitruncated 7-simplex

Tritruncated 7-simplex
Orthogonal projections in A7 Coxeter plane

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

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 symbol t{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces16
5-faces
4-faces
Cells350
Faces336
Edges196
Vertices56
Vertex figureElongated 5-simplex pyramid
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

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

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Bitruncated 7-simplex

Bitruncated 7-simplex
Typeuniform 7-polytope
Schläfli symbol 2t{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges588
Vertices168
Vertex figure
Coxeter groupsA7, [3,3,3,3,3,3]
Propertiesconvex, Vertex-transitive

Alternate names

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

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Tritruncated 7-simplex

Tritruncated 7-simplex
Typeuniform 7-polytope
Schläfli symbol 3t{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges980
Vertices280
Vertex figure
Coxeter groupsA7, [3,3,3,3,3,3]
Propertiesconvex, Vertex-transitive

Alternate names

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

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Related polytopes

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

See also

Notes

  1. Klitizing, (x3x3o3o3o3o3o - toc)
  2. Klitizing, (o3x3x3o3o3o3o - roc)
  3. Klitizing, (o3o3x3x3o3o3o - tattoc)

References

External links

Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / E9 / E10 / F4 / G2 Hn
Regular polygon Triangle Square p-gon Hexagon Pentagon
Uniform polyhedron Tetrahedron OctahedronCube Demicube DodecahedronIcosahedron
Uniform 4-polytope 5-cell 16-cellTesseract Demitesseract 24-cell 120-cell600-cell
Uniform 5-polytope 5-simplex 5-orthoplex5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex6-cube 6-demicube 122221
Uniform 7-polytope 7-simplex 7-orthoplex7-cube 7-demicube 132231321
Uniform 8-polytope 8-simplex 8-orthoplex8-cube 8-demicube 142241421
Uniform 9-polytope 9-simplex 9-orthoplex9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplexn-cube n-demicube 1k22k1k21 n-pentagonal polytope
Topics: Polytope familiesRegular polytopeList of regular polytopes and compounds
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