# Order-4 icositetrachoric tetracomb

The **order-4 icositetrachoric tetracomb**, or **sicot**, is a paracompact regular tiling of 4D hyperbolic space. 4 icositetrachora meet at each face, and infinitely many meet at each vertex in a cubic honeycomb arrangement.

Order-4 icositetrachoric tetracomb | |
---|---|

Rank | 5 |

Type | Regular, paracompact |

Space | Hyperbolic |

Notation | |

Bowers style acronym | Sicot |

Coxeter diagram | o4o3o4o3x () |

Schläfli symbol | {3,4,3,4} |

Elements | |

Tera | MN icositetrachora |

Cells | 12MN octahedra |

Faces | 24MN triangles |

Edges | 12MN |

Vertices | 24N |

Vertex figure | Cubic honeycomb, edge length 1 |

Measures (edge length 1) | |

Circumradius | 0 |

Related polytopes | |

Army | Sicot |

Regiment | Sicot |

Dual | Cubic honeycomb tetracomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | [4,3,4,3] |

Convex | Yes |

## Represenations edit

An order-4 icositetrachoric tetracomb has the following Coxeter diagrams:

- o4o3o4o3x ( ) (full symmetry)
- o3o4o3x *b3o ( ) (facets of alternating types)
- x3o4o3o4o3*a ( ) (x4o3o4x ( ) verf)

## External links edit

- Klitzing, Richard. "sicot".
- Wikipedia contributors. "Order-4 24-cell honeycomb".