# Prismatotruncated hexateron

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Prismatotruncated hexateron | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Pattix |

Coxeter diagram | x3x3o3x3o () |

Elements | |

Tera | 15 octahedral prisms, 20 triangular-hexagonal duoprisms, 6 small rhombated pentachora, 6 prismatorhombated pentachora |

Cells | 60+60+60 triangular prisms, 30 octahedra, 60 hexagonal prisms, 15 truncated tettrahedra, 30 cuboctahedra |

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

Edges | 90+180+360 |

Vertices | 180 |

Vertex figure | Wedge pyramid, edge lengths 1 (base square and top edge of wedge), √2 (sides of wedge and lacings to square), and √3 (lacings to top edge) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Ope–trip–thiddip: 135° |

Srip–oct–ope: | |

Srip–trip–thiddip: | |

Prip–hip–thiddip: | |

Prip–trip–ope: | |

Prip–co–srip: | |

Prip–tut–prip: | |

Central density | 1 |

Number of external pieces | 47 |

Level of complexity | 45 |

Related polytopes | |

Army | Pattix |

Regiment | Pattix |

Dual | Notch-pyramidal hecatonoctacontateron |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{5}, order 720 |

Convex | Yes |

Nature | Tame |

The **prismatotruncated hexateron**, or **pattix**, also called the **runcitruncated 5-simplex**, is a convex uniform polyteron. It consists of 15 octahedral prisms, 20 triangular-hexagonal duoprisms, 6 small rhombated pentachora, and 6 prismatorhombated pentachora. One small rhombated pentachoron, 1 octahedral prism, 2 prismatorhombated pentachora, and 2 triangular-hexagonal duoprisms join at each vertex. As the name suggests, it is the runcitruncation of the hexateron.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A prismatotruncated hexateron has the following Coxeter diagrams:

- x3x3o3x3o (full symmetry)
- xuxx3ooxx3xxxo3ooox&#xt (A
_{4}axial, small rhombated pentachoron-first)

## Gallery[edit | edit source]

## Related polytopes[edit | edit source]

The prismatotruncated hexateron is the colonel of a regiment of 7 members.

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]

- Klitzing, Richard. "pattix".

- Wikipedia Contributors. "Runcitruncated 5-simplex".