# Stericated 6-cubes

| 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 |
| Orthogonal projections in B$_6$ Coxeter plane |||
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 | B$_6$, [4,3,3,3,3] |
| Properties | convex |

### Alternate names

* Small cellated hexeract (Acronym: scox) (Jonathan Bowers)

### Images

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

## Steritruncated 6-cube

Steritruncated 6-cube :
| Type | uniform 6-polytope |
| Schläfli symbol | t$_{0,1,4}${4,3,3,3,3} |
| Coxeter-Dynkin diagrams | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 19200 |
| Vertices | 3840 |
| Vertex figure | |
| Coxeter groups | B$_6$, [4,3,3,3,3] |
| Properties | convex |

### Alternate names

* Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_6$ | B$_5$ | B$_4$ |
| Graph | | | |
| Dihedral symmetry | [12] | [10] | [8] |
| Coxeter plane | B$_3$ | B$_2$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| 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 | B$_6$, [4,3,3,3,3] |
| Properties | convex |

### Alternate names

* Cellirhombated hexeract (Acronym: crax) (Jonathan Bowers)

### Images

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

## Stericantitruncated 6-cube

stericantitruncated 6-cube :
| Type | uniform 6-polytope |
| Schläfli symbol | t$_{0,1,2,4}${4,3,3,3,3} |
| Coxeter-Dynkin diagrams | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 46080 |
| Vertices | 11520 |
| Vertex figure | |
| Coxeter groups | B$_6$, [4,3,3,3,3] |
| Properties | convex |

### Alternate names

* Celligreatorhombated hexeract (Acronym: cagorx) (Jonathan Bowers)

### Images

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

## Steriruncinated 6-cube

steriruncinated 6-cube :
| Type | uniform 6-polytope |
| Schläfli symbol | t$_{0,3,4}${4,3,3,3,3} |
| Coxeter-Dynkin diagrams | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 15360 |
| Vertices | 3840 |
| Vertex figure | |
| Coxeter groups | B$_6$, [4,3,3,3,3] |
| Properties | convex |

### Alternate names

* Celliprismated hexeract (Acronym: copox) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_6$ | B$_5$ | B$_4$ |
| Graph | | | |
| Dihedral symmetry | [12] | [10] | [8] |
| Coxeter plane | B$_3$ | B$_2$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| 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 | B$_6$, [4,3,3,3,3] |
| Properties | convex |

### Alternate names

* Celliprismatotruncated hexeract (Acronym: captix) (Jonathan Bowers)

### Images

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

## Steriruncicantellated 6-cube

steriruncicantellated 6-cube :
| Type | uniform 6-polytope |
| Schläfli symbol | t$_{0,2,3,4}${4,3,3,3,3} |
| Coxeter-Dynkin diagrams | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 40320 |
| Vertices | 11520 |
| Vertex figure | |
| Coxeter groups | B$_6$, [4,3,3,3,3] |
| Properties | convex |

### Alternate names

* Celliprismatorhombated hexeract (Acronym: coprix) (Jonathan Bowers)

### Images

orthographic projections :
| Coxeter plane | B$_6$ | B$_5$ | B$_4$ |
| Graph | | | |
| Dihedral symmetry | [12] | [10] | [8] |
| Coxeter plane | B$_3$ | B$_2$ |
| Graph | | |
| Dihedral symmetry | [6] | [4] |
| Coxeter plane | A$_5$ | A$_3$ |
| 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 | B$_6$, [4,3,3,3,3] |
| Properties | convex |

### Alternate names

* Great cellated hexeract (Acronym: gocax) (Jonathan Bowers)

### Images

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

## Related polytopes

These polytopes are from a set of 63 uniform 6-polytopes generated from the B$_6$ Coxeter plane, including the regular 6-cube or 6-orthoplex.
B6 polytopes :
| β$_6$ | t$_1$β$_6$ | t$_2$β$_6$ | t$_2$γ$_6$ | t$_1$γ$_6$ | γ$_6$ | t$_{0,1}$β$_6$ | t$_{0,2}$β$_6$ |
| t$_{1,2}$β$_6$ | t$_{0,3}$β$_6$ | t$_{1,3}$β$_6$ | t$_{2,3}$γ$_6$ | t$_{0,4}$β$_6$ | t$_{1,4}$γ$_6$ | t$_{1,3}$γ$_6$ | t$_{1,2}$γ$_6$ |
| t$_{0,5}$γ$_6$ | t$_{0,4}$γ$_6$ | t$_{0,3}$γ$_6$ | t$_{0,2}$γ$_6$ | t$_{0,1}$γ$_6$ | t$_{0,1,2}$β$_6$ | t$_{0,1,3}$β$_6$ | t$_{0,2,3}$β$_6$ |
| t$_{1,2,3}$β$_6$ | t$_{0,1,4}$β$_6$ | t$_{0,2,4}$β$_6$ | t$_{1,2,4}$β$_6$ | t$_{0,3,4}$β$_6$ | t$_{1,2,4}$γ$_6$ | t$_{1,2,3}$γ$_6$ | t$_{0,1,5}$β$_6$ |
| t$_{0,2,5}$β$_6$ | t$_{0,3,4}$γ$_6$ | t$_{0,2,5}$γ$_6$ | t$_{0,2,4}$γ$_6$ | t$_{0,2,3}$γ$_6$ | t$_{0,1,5}$γ$_6$ | t$_{0,1,4}$γ$_6$ | t$_{0,1,3}$γ$_6$ |
| t$_{0,1,2}$γ$_6$ | t$_{0,1,2,3}$β$_6$ | t$_{0,1,2,4}$β$_6$ | t$_{0,1,3,4}$β$_6$ | t$_{0,2,3,4}$β$_6$ | t$_{1,2,3,4}$γ$_6$ | t$_{0,1,2,5}$β$_6$ | t$_{0,1,3,5}$β$_6$ |
| t$_{0,2,3,5}$γ$_6$ | t$_{0,2,3,4}$γ$_6$ | t$_{0,1,4,5}$γ$_6$ | t$_{0,1,3,5}$γ$_6$ | t$_{0,1,3,4}$γ$_6$ | t$_{0,1,2,5}$γ$_6$ | t$_{0,1,2,4}$γ$_6$ | t$_{0,1,2,3}$γ$_6$ |
| t$_{0,1,2,3,4}$β$_6$ | t$_{0,1,2,3,5}$β$_6$ | t$_{0,1,2,4,5}$β$_6$ | t$_{0,1,2,4,5}$γ$_6$ | t$_{0,1,2,3,5}$γ$_6$ | t$_{0,1,2,3,4}$γ$_6$ | t$_{0,1,2,3,4,5}$γ$_6$ |