Cantellated 6-cubes


6-cube

Cantellated 6-cube

Bicantellated 6-cube

6-orthoplex

Cantellated 6-orthoplex

Bicantellated 6-orthoplex

Cantitruncated 6-cube

Bicantitruncated 6-cube

Bicantitruncated 6-orthoplex

Cantitruncated 6-orthoplex
Orthogonal projections in B6 Coxeter plane

In six-dimensional geometry, a cantellated 6-cube is a convex uniform 6-polytope, being a cantellation of the regular 6-cube.

There are 8 cantellations for the 6-cube, including truncations. Half of them are more easily constructed from the dual 5-orthoplex.

Cantellated 6-cube

Cantellated 6-cube
Typeuniform 6-polytope
Schläfli symbol rr{4,3,3,3,3}
or
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges4800
Vertices960
Vertex figure
Coxeter groupsB6, [3,3,3,3,4]
Propertiesconvex

Alternate names

Images

orthographic projections
Coxeter plane B6 B5 B4
Graph
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Bicantellated 6-cube

Cantellated 6-cube
Typeuniform 6-polytope
Schläfli symbol 2rr{4,3,3,3,3}
or
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB6, [3,3,3,3,4]
Propertiesconvex

Alternate names

Images

orthographic projections
Coxeter plane B6 B5 B4
Graph
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Cantitruncated 6-cube

Cantellated 6-cube
Typeuniform 6-polytope
Schläfli symbol tr{4,3,3,3,3}
or
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB6, [3,3,3,3,4]
Propertiesconvex

Alternate names

Images

orthographic projections
Coxeter plane B6 B5 B4
Graph
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Bicantitruncated 6-cube

Cantellated 6-cube
Typeuniform 6-polytope
Schläfli symbol 2tr{4,3,3,3,3}
or
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB6, [3,3,3,3,4]
Propertiesconvex

Alternate names

Images

orthographic projections
Coxeter plane B6 B5 B4
Graph
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

These polytopes are part of a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.

Notes

  1. Klitzing, (o3o3o3x3o4x - srox)
  2. Klitzing, (o3o3x3o3x4o - saborx)
  3. Klitzing, (o3o3o3x3x4x - grox)
  4. Klitzing, (o3o3x3x3x4o - gaborx)

References

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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