# Truncated hexateron

Jump to navigation
Jump to search

Truncated hexateron | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Tix |

Coxeter diagram | x3x3o3o3o () |

Elements | |

Tera | 6 pentachora, 6 truncated pentachora |

Cells | 30 tetrahedra, 15 truncated tetrahedra |

Faces | 60 triangles, 20 hexagons |

Edges | 15+60 |

Vertices | 30 |

Vertex figure | Tetrahedral pyramid, edge lengths 1 (base) and √3 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tip–tet–pen: |

Tip–tut–tip: | |

Central density | 1 |

Number of external pieces | 12 |

Level of complexity | 5 |

Related polytopes | |

Army | Tix |

Regiment | Tix |

Dual | Pentakis hexateron |

Conjugate | None |

Abstract & topological properties | |

Flag count | 3600 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{5}, order 720 |

Convex | Yes |

Nature | Tame |

The **truncated hexateron**, or **tix**, also called the **truncated 5-simplex**, is a convex uniform polyteron. It consists of 6 regular pentachora and 6 truncated pentachora. One pentachoron and 4 truncated pentachora join at each vertex. As the name suggests, it is the truncation of the hexateron.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A truncated hexateron has the following Coxeter diagrams:

- x3x3o3o3o (full symmetry)
- xux3oox3ooo3ooo&#xt (A
_{4}axial, pentachoron-first) - xuxo oxux3ooox3oooo&#xt (A
_{3}×A_{1}axial, edge-first) - xuxo3xooo ooox3oxux&#xt (A
_{2}×A_{2}axial, hexagon-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" (#13).

- Klitzing, Richard. "tix".

- Wikipedia Contributors. "Truncated 5-simplex".