# Great birhombidodecateron

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Great birhombidodecateron | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gibrid |

Coxeter diagram | o3x3x3x3o () |

Elements | |

Tera | 20 triangular duoprisms, 12 great rhombated pentachora |

Cells | 120 triangular prisms, 30 truncated tetrahedra, 30 truncated octahedra |

Faces | 120 triangles, 180 squares, 120 hexagons |

Edges | 90+360 |

Vertices | 180 |

Vertex figure | Tetragonal disphenoidal pyramid, edge lengths 1 (base edges of disphenoid), √2 (sides of disphenoid), and √3 (sides of pyramid) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Grip–trip–triddip: |

Grip–toe–grip: | |

Grip–tut–grip: | |

Central density | 1 |

Number of external pieces | 32 |

Level of complexity | 15 |

Related polytopes | |

Army | Gibrid |

Regiment | Gibrid |

Dual | Disphenoidal pyramidal hecatonoctacontateron |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{5}×2, order 1440 |

Convex | Yes |

Nature | Tame |

The **great birhombidodecateron**, or **gibrid**, also called the **great birhombated hexateron** or **bicantitruncated 5-simplex**, is a convex uniform polyteron. It consists of 20 triangular duoprisms and 12 great rhombated pentachora. 1 triangular duoprism and 4 great rhombated pentachora join at each vertex. As the name suggests, it is the bicantitruncation of the hexateron. It is also the truncated dodecateron.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A great birhombidodecateron has the following Coxeter diagrams:

- o3x3x3x3o (full symmetry)
- xooo3xuxx3xxux3ooox&#xt (A
_{4}axial, great rhombated 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" (#729).

- Klitzing, Richard. "gibrid".

- Wikipedia Contributors. "Bicantitruncated 5-simplex".