# Celligreatorhombated tesseractic tetracomb

The **celligreatorhombated tesseractic tetracomb** or **cagratit**, also called the **stericantitruncated tesseractic tetracomb**, is a convex uniform tetracomb. 1 great rhombated tesseract, 1 prismatorhombated tesseract, 1 small rhombicuboctahedral prism, 2 great rhombicuboctahedral prisms, and 1 square-octagonal duoprism join at each vertex of this tessellation. As the name suggests, it is the stericantitruncation of the tesseractic tetracomb.

Celligreatorhombated tesseractic tetracomb | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Cagratit |

Coxeter diagram | x4x3x3o4x () |

Elements | |

Tera | 6N square-octagonal duoprisms, 4N small rhombicuboctahedral prisms, 4N great rhombicuboctahedral prisms, N great rhombated tesseracts, N prismatorhombated tesseracts |

Cells | 32N triangular prisms, 24N+24N+48N cubes, 32N hexagonal prisms, 16N truncated tetrahedra, 24N octagonal prisms, 8N small rhombicuboctahedra, 8N great rhombicuboctahedra |

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

Edges | 96N+96N+192N+192N |

Vertices | 192N |

Vertex figure | Isosceles trapezoidal pyramidal pyramid, base edge lengths 1, √2, √2, √2, remaining edge lengths √2 (6), √3 (2), and √2+√2 (1) |

Related polytopes | |

Army | Cagratit |

Regiment | Cagratit |

Conjugate | Quasicelligreatoquasirhombated tesseractic tetracomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | R_{5} |

Convex | Yes |

Nature | Tame |

## Vertex coordinates edit

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

- ,

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

## External links edit

- Klitzing, Richard. "cagratit".
- Wikipedia contributors. "Stericantitruncated tesseractic honeycomb".