# Rectified tesseractic tetracomb

Jump to navigation
Jump to search

Rectified tesseractic tetracomb | |
---|---|

Rank | 5 |

Type | Quasiregular |

Space | Euclidean |

Notation | |

Bowers style acronym | Rittit |

Coxeter diagram | o4x3o3o4o () |

Elements | |

Tera | N hexadecachora, N rectified tesseracts |

Cells | 16N tetrahedra, 4N cuboctahedra |

Faces | 32N triangles, 6N squares |

Edges | 24N |

Vertices | 4N |

Vertex figure | Octahedral prism, edge lengths 1 (base) and √2 (sides |

Related polytopes | |

Army | Rittit |

Regiment | Rittit |

Dual | Joined tesseractic tetracomb |

Conjugate | None |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | R_{5} |

Convex | Yes |

Nature | Tame |

The **rectified tesseractic tetracomb**, or **rittit**, is a convex uniform tetracomb. 2 hexadecachora and 8 rectified tesseracts join at each vertex of this tessellation. As the name suggests, it is the rectification of the tesseractic tetracomb.

## Vertex coordinates[edit | edit source]

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

- o4x3o3o4o () (full symmetry)
- o3o3x4o *b3o () (half symmetry, tetratetrahedral prism verf)
- x3o3o4o *b3x () (half symmetry, octahedral frustum verf)
- x3o3x *b3o *b3o () (quarter symmetry, tetratetrahedral frustum verf)

## External links[edit | edit source]

- Klitzing, Richard. "rittit".
- Wikipedia contributors. "Rectified tesseractic honeycomb".