# Great rhombated hexateron

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Great rhombated hexateron | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Garx |

Coxeter diagram | x3x3x3o3o () |

Elements | |

Tera | 15 tetrahedral prisms, 6 truncated pentachora, 6 great rhombated pentachora |

Cells | 30 tetrahedra, 60 triangular prisms, 30 truncated tetrahedra, 15 truncated octahedra |

Faces | 120 triangles, 90 squares, 20+60 hexagons |

Edges | 60+60+180 |

Vertices | 120 |

Vertex figure | Triangular pyramidal pyramid, edge lengths 1 (base), √2 (sides of pyramid 1), and √3 (sides of pyramid 2 and lacing between apices) |

Measures (edge length 1) | |

Circumradius | 2 |

Hypervolume | |

Diteral angles | Tip–tet–tepe: |

Grip–trip–tepe: | |

Grip–tut–tip: | |

Grip–toe–grip: | |

Central density | 1 |

Number of external pieces | 27 |

Level of complexity | 20 |

Related polytopes | |

Army | Garx |

Regiment | Garx |

Dual | Triangular-pyramidal pyramidal hecatonicosateron |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{5}, order 720 |

Convex | Yes |

Nature | Tame |

The **great rhombated hexateron**, or **garx**, also called the **cantitruncated 5-simplex**, is a convex uniform polyteron. It consists of 15 tetrahedral prisms, 6 truncated pentachora, and 6 great rhombated pentachora. One truncated pentachoron, 1 tetrahedral prism, and 3 great rhombated pentachora join at each vertex. As the name suggests, it is the cantitruncation of the hexateron.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A great rhombated hexateron has the following Coxeter diagrams:

- x3x3x3o3o (full symmetry)
- xuxx3xxux3ooox3oooo&#xt (A
_{5}axial, truncated pentachoron-first)

## Gallery[edit | edit source]

## Related polytopes[edit | edit source]

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 10: Greater Truncates" (#722).

- Klitzing, Richard. "garx".

- Wikipedia Contributors. "Cantitruncated 5-simplex".