# Great rhombated tesseractic tetracomb

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Great rhombated tesseractic tetracomb | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Grittit |

Coxeter diagram | x4x3x3o4o () |

Elements | |

Tera | 4N octahedral prisms, N truncated hexadecachora, N great rhombated tesseracts |

Cells | 32N triangular prisms, 8N octahedra, 16N truncated tetrahedra, 4N great rhombicuboctahedra |

Faces | 64N triangles, 48N squares, 32N hexagons, 6N octagons |

Edges | 24N+24N+96N |

Vertices | 48N |

Vertex figure | Square pyramidal pyramid, edge lengths 1 (base), √2 (sides of pyramid 1), √3 (sides of pyramid 2), and √2+√2 (lacing between apices) |

Related polytopes | |

Army | Grittit |

Regiment | Grittit |

Conjugate | Great quasirhombated tesseractic tetracomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | R_{5} |

Convex | Yes |

The **great rhombated tesseractic tetracomb** or **grittit**, also called the **cantitruncated tesseractic tetracomb**, is a convex uniform tetracomb. 4 great rhombated tesseracts, 1 truncated hexadecachoron, and 1 octahedral prism join at each vertex of this tessellation. As the name suggests, it is the cantitruncation of the tesseractic tetracomb.

## Vertex coordinates[edit | edit source]

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

- x4x3x3o4o (full symmetry)
- o3x3o *b3x4x (half symmetry)

## Related polytopes[edit | edit source]

Name | OBSA | CD diagram | Picture |
---|---|---|---|

Tesseractic tetracomb | test | ||

Rectified tesseractic tetracomb | rittit | ||

Icositetrachoric tetracomb | icot | ||

Truncated tesseractic tetracomb | tattit | ||

Bitruncated tesseractic tetracomb | batitit | ||

Small rhombated tesseractic tetracomb | srittit | ||

Rectified icositetrachoric tetracomb | ricot | ||

Great rhombated tesseractic tetracomb | grittit | ||

Truncated icositetrachoric tetracomb | ticot | ||

Small prismated tesseractic tetracomb | sidpitit | ||

Prismatotruncated tesseractic tetracomb | potatit | ||

Prismatorhombated tesseractic tetracomb | prittit | ||

Great prismated tesseractic tetracomb | gippittit | ||

Tesseractic tetracomb | test | ||

Celliprismated tesseractic tetracomb | capotat | ||

Cellirhombated tesseractic tetracomb | scartit | ||

Celligreatorhombated tesseractic tetracomb | gicartit | ||

Celliprismatotruncated tesseractic tetracomb | captatit | ||

Great cellated tesseractic tetracomb | otatit |

## External links[edit | edit source]

- Klitzing, Richard. "grittit".

- Wikipedia Contributors. "Cantitruncated tesseractic honeycomb".