# Celligreatorhombated hexateron

Celligreatorhombated hexateron | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Cograx |

Coxeter diagram | x3x3x3o3x () |

Elements | |

Tera | 20 triangular-hexagonal duoprisms, 15 cuboctahedral prisms, 15 truncated octahedral prisms, 6 great rhombated pentachora, 6 prismatorhombated pentachora |

Cells | 60+60+60 triangular prisms, 90 cubes, 60+60 hexagonal prisms, 30 truncated tetrahedra, 30 cuboctahedra, 30 truncated octahedron |

Faces | 120+120 triangles, 180+180+180+180 squares, 60+120 hexagons |

Edges | 180+180+360+360 |

Vertices | 360 |

Vertex figure | Skew rectangular pyramidal pyramid, base edge lengths 1 and √2, remaining edge lengths √2 (6) and √3 (3) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tope–hip–thiddip: 135° |

Cope–trip–thiddip: 135° | |

Prip–co–cope: | |

Grip–toe–tope: | |

Cope–cube–tope: 120° | |

Prip–hip–thiddip: | |

Grip–trip–thiddip: | |

Prip–trip–cope: | |

Prip–tut–grip: | |

Central density | 1 |

Number of external pieces | 62 |

Level of complexity | 80 |

Related polytopes | |

Army | Cograx |

Regiment | Cograx |

Dual | Deltopyramidal pyramidal triacosihexecontateron |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{5}, order 720 |

Convex | Yes |

Nature | Tame |

The **celligreatorhombated hexateron**, or **cograx**, also called the **stericantitruncated 5-simplex**, is a convex uniform polyteron. It consists of 20 triangular-hexagonal duoprisms, 15 cuboctahedral prisms, 15 truncated octahedral prisms, 6 great rhombated pentachora, and 6 prismatorhombated pentachora. 1 prismatorhombated pentachoron, 1 cuboctahedral prism, 1 great rhombated pentachoron, 1 triangular-hexagonal duoprism, and 2 truncated octahedral prisms join at each vertex. As the name suggests, it is the stericantitruncation of the hexateron.

## Vertex coordinates[edit | edit source]

The vertices of a celligreatorhombated hexateron of edge length 1 can be given in 6 dimensions as all permutations of:

## Gallery[edit | edit source]

## Related polytopes[edit | edit source]

The celligreatorhombated hexateron is the colonel of a three-member regiment that also includes the retrocelligreatorhombated hexateron and lepidocelligreatorhombated hexateron.

Name | OBSA | CD diagram | Picture |
---|---|---|---|

Hexateron | hix | ||

Rectified hexateron | rix | ||

Dodecateron | dot | ||

Rectified hexateron | rix | ||

Hexateron | hix | ||

Truncated hexateron | tix | ||

Bitruncated hexateron | bittix | ||

Bitruncated hexateron | bittix | ||

Truncated hexateron | tix | ||

Small rhombated hexateron | sarx | ||

Small birhombidodecateron | sibrid | ||

Small rhombated hexateron | sarx | ||

Great rhombated hexateron | garx | ||

Great birhombidodecateron | gibrid | ||

Great rhombated hexateron | garx | ||

Small prismated hexateron | spix | ||

Small prismated hexateron | spix | ||

Prismatotruncated hexateron | pattix | ||

Prismatorhombated hexateron | pirx | ||

Prismatorhombated hexateron | pirx | ||

Prismatotruncated hexateron | pattix | ||

Great prismated hexateron | gippix | ||

Great prismated hexateron | gippix | ||

Small cellidodecateron | scad | ||

Celliprismated hexateron | cappix | ||

Cellirhombidodecateron | card | ||

Celligreatorhombated hexateron | cograx | ||

Celliprismated hexateron | cappix | ||

Celliprismatotruncatododecateron | captid | ||

Celligreatorhombated hexateron | cograx | ||

Great cellidodecateron | gocad |

## External links[edit | edit source]

- Bowers, Jonathan. "Category 13: Prismatorhombates and Kin" (#841).

- Klitzing, Richard. "cograx".

- Wikipedia Contributors. "Stericantitruncated 5-simplex".