# Hexicated 7-cubes

Orthogonal projections in B$_4$ Coxeter plane :
| 7-cube | Hexicated 7-cube | Hexitruncated 7-cube | Hexicantellated 7-cube |
| Hexiruncinated 7-cube | Hexicantitruncated 7-cube | Hexiruncitruncated 7-cube | Hexiruncicantellated 7-cube |
| Hexisteritruncated 7-cube | Hexistericantellated 7-cube | Hexipentitruncated 7-cube | Hexiruncicantitruncated 7-cube |
| Hexistericantitruncated 7-cube | Hexisteriruncitruncated 7-cube | Hexisteriruncicantellated 7-cube | Hexipenticantitruncated 7-cube |
| Hexipentiruncitruncated 7-cube | Hexisteriruncicantitruncated 7-cube | Hexipentiruncicantitruncated 7-cube | Hexipentistericantitruncated 7-cube |
| Hexipentisteriruncicantitruncated 7-cube (Omnitruncated 7-cube) ||||
In seven-dimensional geometry, a hexicated 7-cube is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-cube.
There are 32 hexications for the 7-cube, including all permutations of truncations, cantellations, runcinations, sterications, and pentellations. 20 are represented here, while 12 are more easily constructed from the 7-orthoplex.
The simple hexicated 7-cube is also called an expanded 7-cube, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 7-cube. The highest form, the hexipentisteriruncicantitruncated 7-cube is more simply called a omnitruncated 7-cube with all of the nodes ringed.
These polytope are among a family of 127 uniform 7-polytopes with B$_7$ symmetry.

## Hexicated 7-cube

Hexicated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,6}${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 |
In seven-dimensional geometry, a hexicated 7-cube is a convex uniform 7-polytope, a hexication (6th order truncation) of the regular 7-cube, or alternately can be seen as an expansion operation.

### Alternate names

* Small petated 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] |

## Hexitruncated 7-cube

hexitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,6}${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

* Petitruncated 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] |

## Hexicantellated 7-cube

Hexicantellated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,2,6}${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

* Petirhombated 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] |

## Hexiruncinated 7-cube

Hexiruncinated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,3,6}${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

* Petiprismated hepteract (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] |

## Hexicantitruncated 7-cube

Hexicantitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,2,6}${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

* Petigreatorhombated 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] |

## Hexiruncitruncated 7-cube

Hexiruncitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,3,6}${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

* Petiprismatotruncated 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] |

## Hexiruncicantellated 7-cube

Hexiruncicantellated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,2,3,6}${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 |
In seven-dimensional geometry, a hexiruncicantellated 7-cube is a uniform 7-polytope.

### Alternate names

* Petiprismatorhombated 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] |

## Hexisteritruncated 7-cube

hexisteritruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,4,6}${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

* Peticellitruncated 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] |

## Hexistericantellated 7-cube

hexistericantellated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,2,4,6}${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

* Peticellirhombihepteract (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] |

## Hexipentitruncated 7-cube

Hexipentitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,5,6}${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

* Petiteritruncated 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] |

## Hexiruncicantitruncated 7-cube

Hexiruncicantitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,2,3,6}${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

* Petigreatoprismated 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] |

## Hexistericantitruncated 7-cube

Hexistericantitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,2,4,6}${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

* Peticelligreatorhombated hepteract (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] |

## Hexisteriruncitruncated 7-cube

Hexisteriruncitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,3,4,6}${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

* Peticelliprismatotruncated hepteract (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] |

## Hexisteriruncicantellated 7-cube

Hexisteriruncitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,2,3,4,6}${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

* Peticelliprismatorhombihepteract (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] |

## Hexipenticantitruncated 7-cube

hexipenticantitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,2,5,6}${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

* Petiterigreatorhombated 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] |

## Hexipentiruncitruncated 7-cube

Hexisteriruncicantitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,2,3,4,6}${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 petacellated hepteract (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] |

## Hexisteriruncicantitruncated 7-cube

Hexisteriruncicantitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,2,3,4,6}${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 petacellated hepteract (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] |

## Hexipentiruncicantitruncated 7-cube

Hexipentiruncicantitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,2,3,5,6}${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

* Petiterigreatoprismated hepteract (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] |

## Hexipentistericantitruncated 7-cube

Hexipentistericantitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,2,4,5,6}${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

* Petitericelligreatorhombihepteract (acronym: putcagroh) (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] |

## Omnitruncated 7-cube

Omnitruncated 7-cube :
| Type | uniform 7-polytope |
| Schläfli symbol | t$_{0,1,2,3,4,5,6}${3$^6$} |
| Coxeter-Dynkin diagrams | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure | |
| Coxeter groups | B$_7$, [4,3$^5$] |
| Properties | convex |
The omnitruncated 7-cube is the largest uniform 7-polytope in the B$_7$ symmetry of the regular 7-cube. It can also be called the hexipentisteriruncicantitruncated 7-cube which is the long name for the omnitruncation for 7 dimensions, with all reflective mirrors active.

### Alternate names

* Great petated hepteract (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] |