# Stericated 6-cubes

(Redirected from Stericantitruncated 6-cube)
 Orthogonal projections in B6 Coxeter plane 6-cube Stericated 6-cube Steritruncated 6-cube Stericantellated 6-cube Stericantitruncated 6-cube Steriruncinated 6-cube Steriruncitruncated 6-cube Steriruncicantellated 6-cube Steriruncicantitruncated 6-cube

In six-dimensional geometry, a stericated 6-cube is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-cube.

There are 8 unique sterications for the 6-cube with permutations of truncations, cantellations, and runcinations.

## Stericated 6-cube

Stericated 6-cube
Type uniform 6-polytope
Schläfli symbol 2r2r{4,3,3,3,3}
Coxeter-Dynkin diagrams

5-faces
4-faces
Cells
Faces
Edges 5760
Vertices 960
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

### Alternate names

• Small cellated hexeract (Acronym: scox) (Jonathan Bowers)[1]

### 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]

## Steritruncated 6-cube

Steritruncated 6-cube
Type uniform 6-polytope
Schläfli symbol t0,1,4{4,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges 19200
Vertices 3840
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

### Alternate names

• Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers)[2]

### 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]

## Stericantellated 6-cube

Stericantellated 6-cube
Type uniform 6-polytope
Schläfli symbol 2r2r{4,3,3,3,3}
Coxeter-Dynkin diagrams

5-faces
4-faces
Cells
Faces
Edges 28800
Vertices 5760
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

### Alternate names

• Cellirhombated hexeract (Acronym: crax) (Jonathan Bowers)[3]

### 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]

## Stericantitruncated 6-cube

stericantitruncated 6-cube
Type uniform 6-polytope
Schläfli symbol t0,1,2,4{4,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges 46080
Vertices 11520
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

### Alternate names

• Celligreatorhombated hexeract (Acronym: cagorx) (Jonathan Bowers)[4]

### 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]

## Steriruncinated 6-cube

steriruncinated 6-cube
Type uniform 6-polytope
Schläfli symbol t0,3,4{4,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges 15360
Vertices 3840
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

### Alternate names

• Celliprismated hexeract (Acronym: copox) (Jonathan Bowers)[5]

### 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]

## Steriruncitruncated 6-cube

steriruncitruncated 6-cube
Type uniform 6-polytope
Schläfli symbol 2t2r{4,3,3,3,3}
Coxeter-Dynkin diagrams

5-faces
4-faces
Cells
Faces
Edges 40320
Vertices 11520
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

### Alternate names

• Celliprismatotruncated hexeract (Acronym: captix) (Jonathan Bowers)[6]

### 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]

## Steriruncicantellated 6-cube

steriruncicantellated 6-cube
Type uniform 6-polytope
Schläfli symbol t0,2,3,4{4,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges 40320
Vertices 11520
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

### Alternate names

• Celliprismatorhombated hexeract (Acronym: coprix) (Jonathan Bowers)[7]

### 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]

## Steriruncicantitruncated 6-cube

Steriuncicantitruncated 6-cube
Type uniform 6-polytope
Schläfli symbol tr2r{4,3,3,3,3}
Coxeter-Dynkin diagrams

5-faces
4-faces
Cells
Faces
Edges 69120
Vertices 23040
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

### Alternate names

• Great cellated hexeract (Acronym: gocax) (Jonathan Bowers)[8]

### 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]

## Related polytopes

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, (x4o3o3o3x3o - scox)
2. ^ Klitzing, (x4x3o3o3x3o - catax)
3. ^ Klitzing, (x4o3x3o3x3o - crax)
4. ^ Klitzing, (x4x3x3o3x3o - cagorx)
5. ^ Klitzing, (x4o3o3x3x3o - copox))
6. ^ Klitzing, (x4x3o3x3x3o - captix)
7. ^ Klitzing, (x4o3x3x3x3o - coprix)
8. ^ Klitzing, (x4x3x3x3x3o - gocax)

## References

• H.S.M. Coxeter:
• H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
• Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
• (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
• (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
• (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
• Norman Johnson Uniform Polytopes, Manuscript (1991)
• N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
• Klitzing, Richard. "6D uniform polytopes (polypeta)".