# Stericated 7-orthoplexes

(Redirected from Steriruncitruncated 7-orthoplex)
Orthogonal projections in B6 Coxeter plane

7-orthoplex

Stericated 7-orthoplex

Steritruncated 7-orthoplex

Bisteritruncated 7-orthoplex

Stericantellated 7-orthoplex

Stericantitruncated 7-orthoplex

Bistericantitruncated 7-orthoplex

Steriruncinated 7-orthoplex

Steriruncitruncated 7-orthoplex

Steriruncicantellated 7-orthoplex

Bisteriruncitruncated 7-orthoplex

Steriruncicantitruncated 7-orthoplex

In seven-dimensional geometry, a stericated 7-orthoplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-orthoplex.

There are 24 unique sterication for the 7-orthoplex with permutations of truncations, cantellations, and runcinations. 14 are more simply constructed from the 7-cube.

This polytope is one of 127 uniform 7-polytopes with B7 symmetry.

## Stericated 7-orthoplex

Stericated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,4{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

### Alternate names

• Small cellated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[1]

### 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]

## Steritruncated 7-orthoplex

steritruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,4{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

### Alternate names

• Cellitruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[2]

### 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]

## Bisteritruncated 7-orthoplex

bisteritruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t1,2,5{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

### Alternate names

• Bicellitruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[3]

### 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]

## Stericantellated 7-orthoplex

Stericantellated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,2,4{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

### Alternate names

• Cellirhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[4]

### 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]

## Stericantitruncated 7-orthoplex

stericantitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,4{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

### Alternate names

• Celligreatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[5]

### 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]

## Bistericantitruncated 7-orthoplex

bistericantitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t1,2,3,5{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

### Alternate names

• Bicelligreatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[6]

### 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]

## Steriruncinated 7-orthoplex

Steriruncinated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,3,4{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

### Alternate names

• Celliprismated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[7]

### Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex
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]

## Steriruncitruncated 7-orthoplex

steriruncitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,3,4{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

### Alternate names

• Celliprismatotruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[8]

### 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]

## Steriruncicantellated 7-orthoplex

steriruncicantellated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,2,3,4{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

### Alternate names

• Celliprismatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[9]

### 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]

## Steriruncicantitruncated 7-orthoplex

steriruncicantitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,3,4{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

### Alternate names

• Great cellated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[10]

### 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. ^ Klitizing, (x3o3o3o3x3o4o - )
2. ^ Klitizing, (x3x3o3o3x3o4o - )
3. ^ Klitizing, (o3x3x3o3o3x4o - )
4. ^ Klitizing, (x3o3x3o3x3o4o - )
5. ^ Klitizing, (x3x3x3o3x3o4o - )
6. ^ Klitizing, (o3x3x3x3o3x4o - )
7. ^ Klitizing, (x3o3o3x3x3o4o - )
8. ^ Klitizing, (x3x3x3o3x3o4o - )
9. ^ Klitizing, (x3o3x3x3x3o4o - )
10. ^ Klitizing, (x3x3x3x3x3o4o - )

## 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. "7D uniform polytopes (polyexa)".