# Stericated 7-cubes

Orthogonal projections in B$_6$ Coxeter plane :
| 7-cube | Stericated 7-cube | Bistericated 7-cube |
| Steritruncated 7-cube | Bisteritruncated 7-cube | Stericantellated 7-cube |
| Bistericantellated 7-cube | Stericantitruncated 7-cube | Bistericantitruncated 7-cube |
| Steriruncinated 7-cube | Steriruncitruncated 7-cube | Steriruncicantellated 7-cube |
| Bisteriruncitruncated 7-cube | Steriruncicantitruncated 7-cube | Bisteriruncicantitruncated 7-cube |
In seven-dimensional geometry, a stericated 7-cube is a convex uniform 7-polytope with 4th-order truncations (sterication) of the regular 7-cube.
There are 24 unique sterication for the 7-cube with permutations of truncations, cantellations, and runcinations. 10 are more simply constructed from the 7-orthoplex.
This polytope is one of 127 uniform 7-polytopes with B$_7$ symmetry.

## Stericated 7-cube

Stericated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,4}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Small cellated hepteract (acronym: ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |

## Bistericated 7-cube

bistericated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{1,5}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Small bicellated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |

## Steritruncated 7-cube

steritruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,4}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Cellitruncated hepteract (acronym: ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |

## Bisteritruncated 7-cube

bisteritruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{1,2,5}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Bicellitruncated hepteract (acronym: ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |

## Stericantellated 7-cube

Stericantellated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,2,4}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Cellirhombated hepteract (acronym: ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |

## Bistericantellated 7-cube

Bistericantellated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{1,3,5}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Bicellirhombihepteract (acronym: ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |

## Stericantitruncated 7-cube

stericantitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,2,4}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Celligreatorhombated hepteract (acronym: ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |

## Bistericantitruncated 7-cube

bistericantitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{1,2,3,5}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Bicelligreatorhombated hepteract (acronym: ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |

## Steriruncinated 7-cube

Steriruncinated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,3,4}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Celliprismated hepteract (acronym: ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |

## Steriruncitruncated 7-cube

steriruncitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,3,4}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Celliprismatotruncated hepteract (acronym: ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |

## Steriruncicantellated 7-cube

steriruncicantellated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,2,3,4}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Celliprismatorhombated hepteract (acronym: ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |

## Bisteriruncitruncated 7-cube

bisteriruncitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{1,2,4,5}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Bicelliprismatotruncated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |

## Steriruncicantitruncated 7-cube

steriruncicantitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,2,3,4}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Great cellated hepteract (acronym: ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | too complex | too complex |
| Dihedral symmetry | [6] | [4] |

## Bisteriruncicantitruncated 7-cube

bisteriruncicantitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{1,2,3,4,5}${4,3$^5$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |

### Alternate names

* Great bicellated hepteractihecatonicosoctaexon (Acronym ) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_7$ / A$_6$ | B$_6$ / D$_7$ | B$_5$ / D$_6$ / A$_4$ |
| Graph | too complex | | |
| Dihedral symmetry | [14] | [12] | [10] |
| Coxeter plane | B$_4$ / D$_5$ | B$_3$ / D$_4$ / A$_2$ | B$_2$ / D$_3$ |
| Graph | | | |
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |