# Prismatotruncated tesseractic tetracomb

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Prismatotruncated tesseractic tetracomb | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Potatit |

Coxeter diagram | x4x3o3x4o () |

Elements | |

Tera | 6N square-octagonal duoprisms, 4N cuboctahedral prisms, N rectified icositetrachora, N prismatorhombated hexadecachora |

Cells | 32N triangular prisms, 24N+24N cubes, 8N+16N cuboctahedra, 24N octagonal prisms, 4N truncated cubes |

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

Edges | 48N+96N |

Vertices | 32N |

Vertex figure | Wedge pyramid, edge lengths 1 (two edges of base rectangle and top edge of wedge), √2 (sides of wedge, other edges of rectangle base, and lacings to rectangle), and √2+√2 (lacings to top edge) |

Related polytopes | |

Army | Potatit |

Regiment | Potatit |

Conjugate | Quasiprismatotruncated tesseractic tetracomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | R_{5} |

Convex | Yes |

Nature | Tame |

The **prismatotruncated tesseractic tetracomb** or **potatit**, also called the **runcitruncated tesseractic tetracomb** is a convex uniform tetracomb. 1 rectified icositetrachoron, 2 prismatorhombated hexadecachora, 2 square-octagonal duoprisms, and 1 cuboctahedral prism join at each vertex of this tessellation. As the name suggests, it is the runcitruncation of the tesseractic tetracomb.

## Vertex coordinates[edit | edit source]

The vertices of a prismatotruncated 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 prismatotruncated tesseractic tetracomb has the following Coxeter diagrams:

- x4x3o3x4o (full symmetry)
- x3o3x *b3x4x (half symmetry)

## External links[edit | edit source]

- Klitzing, Richard. "potatit".
- Wikipedia contributors. "Runcitruncated tesseractic honeycomb".