Runcinated 7-cubes


7-cube

Runcinated 7-cube

Biruncinated 7-cube

Runcitruncated 7-cube

Biruncitruncated 7-cube

Runcicantellated 7-cube

Biruncicantellated 7-cube

Runcicantitruncated 7-cube

Biruncicantitruncated 7-cube
Orthogonal projections in B7 Coxeter plane

In seven-dimensional geometry, a runcinated 7-cube is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-cube.

There are 16 unique runcinations of the 7-cube with permutations of truncations, and cantellations. 8 are more simply constructed from the 7-orthoplex.

These polytopes are among 127 uniform 7-polytopes with B7 symmetry.

Runcinated 7-cube

Runcinated 7-cube
Typeuniform 7-polytope
Schläfli symbol t0,3{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges33600
Vertices4480
Vertex figure
Coxeter groupsB7, [4,35]
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]

Biruncinated 7-cube

Biruncinated 7-cube
Typeuniform 7-polytope
Schläfli symbol t1,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges67200
Vertices8960
Vertex figure
Coxeter groupsB7, [4,35]
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]

Runcitruncated 7-cube

Runcitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbol t0,1,3{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges73920
Vertices13440
Vertex figure
Coxeter groupsB7, [4,35]
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]

Biruncitruncated 7-cube

Biruncitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbol t1,2,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges134400
Vertices26880
Vertex figure
Coxeter groupsB7, [4,35]
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]

Runcicantellated 7-cube

Runcicantellated 7-cube
Typeuniform 7-polytope
Schläfli symbol t0,2,3{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges53760
Vertices13440
Vertex figure
Coxeter groupsB7, [4,35]
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]

Biruncicantellated 7-cube

biruncicantellated 7-cube
Typeuniform 7-polytope
Schläfli symbol t1,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges120960
Vertices26880
Vertex figure
Coxeter groupsB7, [4,35]
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]

Runcicantitruncated 7-cube

Runcicantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbol t0,1,2,3{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges94080
Vertices26880
Vertex figure
Coxeter groupsB7, [4,35]
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]

Biruncicantitruncated 7-cube

biruncicantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbol t1,2,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges188160
Vertices53760
Vertex figure
Coxeter groupsB7, [4,35]
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]

Notes

  1. Klitzing, (x3o3o3x3o3o4o - spesa)
  2. Klitzing, (o3x3o3o3x3o4o - sibposa)
  3. Klitzing, (x3x3o3x3o3o4o - petsa)
  4. Klitzing, (o3x3x3o3x3o4o - biptesa)
  5. Klitzing, (x3o3x3x3o3o4o - parsa)
  6. Klitzing, (o3o3x3x3o3x4o - bopresa)
  7. Klitzing, (x3x3x3x3o3o4o - gapsa)
  8. Klitzing, (o3x3x3x3x3o3o - gibposa)

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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