# Stericated 6-orthoplexes

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

### Alternate names

* Small cellated hexacontatetrapeton (Acronym: scag) (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-orthoplex

Steritruncated 6-orthoplex :
| Type | uniform 6-polytope |
| Schläfli symbol | t$_{0,1,4}${3,3,3,3,4} |
| 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

* Cellitruncated hexacontatetrapeton (Acronym: catog) (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-orthoplex

Stericantellated 6-orthoplex :
| Type | uniform 6-polytope |
| Schläfli symbols | t$_{0,2,4}${3$^4$,4} rr2r{3,3,3,3,4} |
| 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 hexacontatetrapeton (Acronym: crag) (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-orthoplex

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

### Alternate names

* Celligreatorhombated hexacontatetrapeton (Acronym: cagorg) (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-orthoplex

Steriruncinated 6-orthoplex :
| Type | uniform 6-polytope |
| Schläfli symbol | t$_{0,3,4}${3,3,3,3,4} |
| 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 hexacontatetrapeton (Acronym: copog) (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-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 | B$_6$, [4,3,3,3,3] |
| Properties | convex |

### Alternate names

* Celliprismatotruncated hexacontatetrapeton (Acronym: captog) (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-orthoplex

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

### Alternate names

* Celliprismatorhombated hexacontatetrapeton (Acronym: coprag) (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-orthoplex

Steriuncicantitruncated 6-orthoplex :
| Type | uniform 6-polytope |
| Schläfli symbols | t$_{0,1,2,3,4}${3$^4$,4} tr2r{3,3,3,3,4} |
| Coxeter-Dynkin diagrams | |
| 5-faces | 536: 12 t$_{0,1,2,3}${3,3,3,4} 60×t$_{0,1,2}${3,3,4} × 160 {6}×t$_{0,1,2}${3,3} × 240 {4}×t$_{0,1,2}${3,3} × 64 t$_{0,1,2,3,4}${3$^4$} |
| 4-faces | 8216 |
| Cells | 38400 |
| Faces | 76800 |
| Edges | 69120 |
| Vertices | 23040 |
| Vertex figure | irregular 5-simplex |
| Coxeter groups | B$_6$, [4,3,3,3,3] |
| Properties | convex |

### Alternate names

* Great cellated hexacontatetrapeton (Acronym: gocog) (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] |

### 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 [3$^{2,1,1,1}$]$^+$ 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 B$_6$ Coxeter plane, including the regular 6-orthoplex 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$_6$ |