# Prismatorhombated tesseractic tetracomb

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Prismatorhombated tesseractic tetracomb | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Prittit |

Coxeter diagram | x4o3x3x4o () |

Elements | |

Tera | 6N tesseracts, 4N truncated octahedral prisms, N tesseractihexadecachora, N prismatorhombated tesseracts |

Cells | 24N+24N cubes, 32N hexagonal prisms, 16N truncated tetrahedra, 4N cuboctahedra, 8N truncated octahedra |

Faces | 32N triangles, 24N+24N+48N+96N squares, 64N hexagons |

Edges | 96N+96N+96N |

Vertices | 96N |

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

Related polytopes | |

Army | Prittit |

Regiment | Prittit |

Conjugate | Quasiprismatorhombated tesseractic tetracomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | R_{5} |

Convex | Yes |

The **prismatorhombated tesseractic tetracomb** or **prittit**, also called the **runcicantellated tesseractic tetracomb** is a convex uniform tetracomb. 1 tesseractihexadecachoron, 2 prismatorhombated tesseracts, 1 truncated octahedral prism, and 1 tesseract (as a square duoprism) join at each vertex of this tessellation. As the name suggests, it is the runcicantellation of the tesseractic tetracomb.

## Vertex coordinates[edit | edit source]

The vertices of a prismatorhombated tesseractic tetracomb of edge length 1 are given by all permutations of:

Where i, j, k, and l range over the integers.

## Representations[edit | edit source]

A prismatorhombated tesseractic tetracomb has the following Coxeter diagrams:

- x4o3x3x4o (full symmetry)
- x3x3x *b3o4x (half symmetry)

## Related polytopes[edit | edit source]

Name | OBSA | CD diagram | Picture |
---|---|---|---|

Tesseractic tetracomb | test | ||

Rectified tesseractic tetracomb | rittit | ||

Icositetrachoric tetracomb | icot | ||

Truncated tesseractic tetracomb | tattit | ||

Bitruncated tesseractic tetracomb | batitit | ||

Small rhombated tesseractic tetracomb | srittit | ||

Rectified icositetrachoric tetracomb | ricot | ||

Great rhombated tesseractic tetracomb | grittit | ||

Truncated icositetrachoric tetracomb | ticot | ||

Small prismated tesseractic tetracomb | sidpitit | ||

Prismatotruncated tesseractic tetracomb | potatit | ||

Prismatorhombated tesseractic tetracomb | prittit | ||

Great prismated tesseractic tetracomb | gippittit | ||

Tesseractic tetracomb | test | ||

Celliprismated tesseractic tetracomb | capotat | ||

Cellirhombated tesseractic tetracomb | scartit | ||

Celligreatorhombated tesseractic tetracomb | gicartit | ||

Celliprismatotruncated tesseractic tetracomb | captatit | ||

Great cellated tesseractic tetracomb | otatit |

## External links[edit | edit source]

- Klitzing, Richard. "prittit".

- Wikipedia Contributors. "Runcicantellated tesseractic honeycomb".