Cantellated 7-orthoplexes


7-orthoplex

Cantellated 7-orthoplex

Bicantellated 7-orthoplex

Birectified 7-orthoplex

Cantitruncated 7-orthoplex

Bicantitruncated 7-orthoplex

Cantellated 7-cube

Bicantellated 7-cube

Tricantellated 7-cube

Cantitruncated 7-cube

Bicantitruncated 7-cube

Tricantitruncated 7-cube
Orthogonal projections in B6 Coxeter plane

In seven-dimensional geometry, a cantellated 7-orthoplex is a convex uniform 7-polytope, being a cantellation of the regular 7-orthoplex.

There are ten degrees of cantellation for the 7-orthoplex, including truncations. Six are most simply constructible from the dual 7-cube.

Cantellated 7-orthoplex

Cantellated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbol rr{3,3,3,3,3,4}
Coxeter-Dynkin diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges7560
Vertices840
Vertex figure
Coxeter groupsB7, [4,3,3,3,3,3]
Propertiesconvex

Alternate names

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Bicantellated 7-orthoplex

Bicantellated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbol 2rr{3,3,3,3,3,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,3,3,3,3,3]
Propertiesconvex

Alternate names

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Cantitruncated 7-orthoplex

Cantitruncated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbol tr{3,3,3,3,3,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges8400
Vertices1680
Vertex figure
Coxeter groupsB7, [4,3,3,3,3,3]
Propertiesconvex

Alternate names

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Bicantitruncated 7-orthoplex

Bicantitruncated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbol 2tr{3,3,3,3,3,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges30240
Vertices6720
Vertex figure
Coxeter groupsB7, [4,3,3,3,3,3]
Propertiesconvex

Alternate names

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Related polytopes

These polytopes are from a family of 127 uniform 7-polytopes with B7 symmetry.

See also

Notes

  1. Klitizing, (o3o3o3o3x3o4x - sarz)
  2. Klitizing, (o3o3o3x3o3x4o - sebraz)
  3. Klitizing, (o3o3o3o3x3x4x - garz)
  4. Klitizing, (o3o3o3x3x3x4o - gebraz)

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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