# Prismatorhombated hexateron

Prismatorhombated hexateron | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Pirx |

Coxeter diagram | x3o3x3x3o () |

Elements | |

Tera | 20 triangular duoprisms, 15 truncated tetrahedral prisms, 6 decachora, 6 prismatorhombated pentachora |

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

Faces | 60+60+60 triangles, 90+180 squares, 120 hexagons |

Edges | 180+180+180 |

Vertices | 180 |

Vertex figure | Skewed rectangular scalene, base edge lengths 1 and √2, opposite edge length 1, lacing lengths √2 and √3 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tuttip–trip–triddip: 135° |

Deca–tut–tuttip: | |

Prip–trip–triddip: | |

Prip–hip–tuttip: | |

Prip–tut–deca: | |

Prip–co–prip: | |

Central density | 1 |

Number of external pieces | 47 |

Level of complexity | 40 |

Related polytopes | |

Army | Pirx |

Regiment | Pirx |

Dual | Rhombiscalenic hecatonicoctacontateron |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{5}, order 720 |

Convex | Yes |

Nature | Tame |

The **prismatorhombated hexateron**, or **pirx**, also called the **runcicantellated 5-simplex**, is a convex uniform polyteron. It consists of 20 triangular duoprisms, 15 truncated tetrahedral prisms, 6 decachora, and 6 prismatorhombated pentachora. 2 prismatorhombated pentachora, 1 decachoron, 1 triangular duoprism, and 2 truncated tetrahedral prisms join at each vertex. As the name suggests, it is the runcicantellation of the hexateron.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A prismatorhombated hexateron has the following Coxeter diagrams:

- x3o3x3x3o (full symmetry)
- oxxx3xxoo3xxux3ooox&#xt (A
_{4}axial, decachoron-first)

## Gallery[edit | edit source]

## Related polytopes[edit | edit source]

The prismatorhombated hexateron is the colonel of a three-member regiment that also includes the retroprismatorhombated hexateron and lepidoprismatorhombated hexateron.

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 13: Prismatorhombates and Kin" (#829).

- Klitzing, Richard. "pirx".

- Wikipedia Contributors. "Runcicantellated 5-simplex".