# Order-4 hecatonicosachoric tetracomb

The **order-4 hecatonicosachoric tetracomb**, or **shitte**, is a compact regular tiling of 4D hyperbolic space. 4 hecatonicosachora meet at each face, and 16 meet at each vertex, forming a hexadecachoron as the vertex figure.

Order-4 hecatonicosachoric tetracomb | |
---|---|

Rank | 5 |

Type | Regular, compact |

Space | Hyperbolic |

Notation | |

Bowers style acronym | Shitte |

Coxeter diagram | x5o3o3o4o () |

Schläfli symbol | {5,3,3,4} |

Elements | |

Tera | 2N hecatonicosachora |

Cells | 120N dodecahedra |

Faces | 360N pentagons |

Edges | 300N |

Vertices | 75N |

Vertex figure | Hexadecachoron, edge length (1+√5)/2 |

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Army | Shitte |

Regiment | Shitte |

Dual | Order-5 tesseractic tetracomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Convex | Yes |

## Representations edit

The order-4 hecatonicosachoric tetracomb has the following Coxeter diagrams:

- x5o3o3o4o ( ) (full symmetry)
- x5o3o3o *c3o ( ) (two types of hecatonicosachora)

## External links edit

- Klitzing, Richard. "o4o3o3o5x".
- Wikipedia contributors. "Order-4 120-cell honeycomb".