# Stericated 6-orthoplexes

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

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

There are 16 unique sterications for the 6-orthoplex with permutations of truncations, cantellations, and runcinations. Eight are better represented from the stericated 6-cube.

## Stericated 6-orthoplex

Stericated 6-orthoplex
Type uniform 6-polytope
Schläfli symbol 2r2r{3,3,3,3,4}
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 hexacontatetrapeton (Acronym: scag) (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-orthoplex

Steritruncated 6-orthoplex
Type uniform 6-polytope
Schläfli symbol t0,1,4{3,3,3,3,4}
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

• Cellitruncated hexacontatetrapeton (Acronym: catog) (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-orthoplex

Stericantellated 6-orthoplex
Type uniform 6-polytope
Schläfli symbols t0,2,4{34,4}
rr2r{3,3,3,3,4}
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 hexacontatetrapeton (Acronym: crag) (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-orthoplex

Stericantitruncated 6-orthoplex
Type uniform 6-polytope
Schläfli symbol t0,1,2,4{3,3,3,3,4}
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 hexacontatetrapeton (Acronym: cagorg) (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-orthoplex

Steriruncinated 6-orthoplex
Type uniform 6-polytope
Schläfli symbol t0,3,4{3,3,3,3,4}
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 hexacontatetrapeton (Acronym: copog) (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-orthoplex

Steriruncitruncated 6-orthoplex
Type uniform 6-polytope
Schläfli symbol 2t2r{3,3,3,3,4}
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 hexacontatetrapeton (Acronym: captog) (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-orthoplex

Steriruncicantellated 6-orthoplex
Type uniform 6-polytope
Schläfli symbol t0,2,3,4{3,3,3,3,4}
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 hexacontatetrapeton (Acronym: coprag) (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-orthoplex

Steriuncicantitruncated 6-orthoplex
Type uniform 6-polytope
Schläfli symbols t0,1,2,3,4{34,4}
tr2r{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces 536:
12 t0,1,2,3{3,3,3,4}
60 {}×t0,1,2{3,3,4}  ×
160 {6}×t0,1,2{3,3}  ×
240 {4}×t0,1,2{3,3}  ×
64 t0,1,2,3,4{34}
4-faces 8216
Cells 38400
Faces 76800
Edges 69120
Vertices 23040
Vertex figure irregular 5-simplex
Coxeter groups B6, [4,3,3,3,3]
Properties convex

### Alternate names

• Great cellated hexacontatetrapeton (Acronym: gocog) (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]

### Snub 6-demicube

The snub 6-demicube defined as an alternation of the omnitruncated 6-demicube is not uniform, but it can be given Coxeter diagram           or             and symmetry [32,1,1,1]+ or [4,(3,3,3,3)+], and constructed from 12 snub 5-demicubes, 64 snub 5-simplexes, 60 snub 24-cell antiprisms, 160 3-s{3,4} duoantiprisms, 240 2-sr{3,3} duoantiprisms, and 11520 irregular 5-simplexes filling the gaps at the deleted vertices.

## Related polytopes

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

## Notes

1. ^ Klitzing, (x3o3o3o3x4o - scag)
2. ^ Klitzing, (x3x3o3o3x4o - catog)
3. ^ Klitzing, (x3o3x3o3x4o - crag)
4. ^ Klitzing, (x3x3x3o3x4o - cagorg)
5. ^ Klitzing, (x3o3o3x3x4o - copog)
6. ^ Klitzing, (x3x3o3x3x4o - captog)
7. ^ Klitzing, (x3o3x3x3x4o - coprag)
8. ^ Klitzing, (x3x3x3x3x4o - gocog)

## 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)".