Runcinated 6-cubes


6-cube

Runcinated 6-cube

Biruncinated 6-cube

Runcinated 6-orthoplex

6-orthoplex

Runcitruncated 6-cube

Biruncitruncated 6-cube

Runcicantellated 6-orthoplex

Runcicantellated 6-cube

Biruncitruncated 6-orthoplex

Runcitruncated 6-orthoplex

Runcicanti-truncated 6-cube

Biruncicanti-truncated 6-cube

Runcicanti-truncated 6-orthoplex
Orthogonal projections in B6 Coxeter plane

In six-dimensional geometry, a runcinated 6-cube is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-cube.

There are 12 unique runcinations of the 6-cube with permutations of truncations, and cantellations. Half are expressed relative to the dual 6-orthoplex.

Runcinated 6-cube

Runcinated 6-cube
TypeUniform 6-polytope
Schläfli symbolt0,3{4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Edges7680
Vertices1280
Vertex figure
Coxeter groupB6 [4,3,3,3,3]
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]

Biruncinated 6-cube

Biruncinated 6-cube
TypeUniform 6-polytope
Schläfli symbolt1,4{4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Edges11520
Vertices1920
Vertex figure
Coxeter groupB6 [4,3,3,3,3]
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]

Runcitruncated 6-cube

Runcitruncated 6-cube
TypeUniform 6-polytope
Schläfli symbolt0,1,3{4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Edges17280
Vertices3840
Vertex figure
Coxeter groupB6 [4,3,3,3,3]
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]

Biruncitruncated 6-cube

Biruncitruncated 6-cube
TypeUniform 6-polytope
Schläfli symbolt1,2,4{4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Edges23040
Vertices5760
Vertex figure
Coxeter groupB6 [4,3,3,3,3]
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]

Runcicantellated 6-cube

Runcicantellated 6-cube
TypeUniform 6-polytope
Schläfli symbolt0,2,3{4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Edges13440
Vertices3840
Vertex figure
Coxeter groupB6 [4,3,3,3,3]
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]

Runcicantitruncated 6-cube

Runcicantitruncated 6-cube
TypeUniform 6-polytope
Schläfli symbolt0,1,2,3{4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Edges23040
Vertices7680
Vertex figure
Coxeter groupB6 [4,3,3,3,3]
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]

Biruncitruncated 6-cube

Biruncitruncated 6-cube
TypeUniform 6-polytope
Schläfli symbolt1,2,3,4{4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Edges23040
Vertices5760
Vertex figure
Coxeter groupB6 [4,3,3,3,3]
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 from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.

Notes

  1. Klitzing, (o3o3x3o3o4x - spox)
  2. Klitzing, (o3x3o3o3x4o - sobpoxog)
  3. Klitzing, (o3o3x3o3x4x - potax)
  4. Klitzing, (o3x3o3x3x4o - boprag)
  5. Klitzing, (o3o3x3x3o4x - prox)
  6. Klitzing, (o3o3x3x3x4x - gippox)
  7. Klitzing, (o3x3x3x3x4o - boprag)

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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