# Bitruncated hexateron

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Bitruncated hexateron | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Bittix |

Coxeter diagram | o3x3x3o3o () |

Elements | |

Tera | 6 truncated pentachora, 6 decachora |

Cells | 15 tetrahedra, 15+30 truncated tetrahedra |

Faces | 20+60 triangles, 60 hexagons |

Edges | 60+90 |

Vertices | 60 |

Vertex figure | Triangular scalene, edge lengths 1 (base triangle and top edge) and √3 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Deca–tut–tip: |

Tip–tet–tip: | |

Deca–tut–deca: | |

Central density | 1 |

Number of external pieces | 12 |

Level of complexity | 10 |

Related polytopes | |

Army | Bittix |

Regiment | Bittix |

Dual | Triangular-scalenic hexecontateron |

Conjugate | None |

Abstract & topological properties | |

Flag count | 7200 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{5}, order 720 |

Convex | Yes |

Nature | Tame |

The **bitruncated hexateron**, or **bittix**, also called the **bitruncated 5-simplex**, is a convex uniform polyteron. It consists of 6 truncated pentachora and 6 decachora. 2 truncated pentachora and 3 decachora join at each vertex. As the name suggests, it is the bitruncation of the hexateron.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A bitruncated hexateron has the following Coxeter diagrams:

- o3x3x3o3o (full symmetry)
- oox3xux3xoo3ooo&#xt (A
_{4}axial, decachoron-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 2: Truncates" (#21).

- Klitzing, Richard. "bittix".

- Wikipedia Contributors. "Bitruncated 5-simplex".