# Great tesseractitesseractihexadecachoron

Great tesseractitesseractihexadecachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Gittith |

Coxeter diagram | o3o3x4/3x4*b () |

Elements | |

Cells | 16 tetrahedra, 8 cubes, 8 great cubicuboctahedra |

Faces | 64 triangles, 48 squares, 24 octagrams |

Edges | 96+96 |

Vertices | 64 |

Vertex figure | Triangular frustum, edge lengths 1 (small base), √2 (large base), and √2–√2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Gocco–3–tet: 120° |

Gocco–8/3–gocco: 90° | |

Gocco–4–cube: 90° | |

Central density | 5 |

Number of external pieces | 152 |

Level of complexity | 30 |

Related polytopes | |

Army | Tat, edge length |

Regiment | Gittith |

Conjugate | Small tesseractitesseractihexadecachoron |

Abstract & topological properties | |

Flag count | 2304 |

Euler characteristic | –24 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | No |

The **great tesseractitesseractihexadecachoron**, or **gittith**, is a nonconvex uniform polychoron that consists of 16 regular tetrahedra, 8 cubes, and 8 great cubicuboctahedra. 1 tetrahedron, 1 cube, and 3 great cubicuboctahedra join at each vertex.

The great tesseractitesseractihexadecachoron contains the vertices and edges of a great cubicuboctahedral prism and square-octagrammic duoprism.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a great tesseractitesseractihexadecachoron with edge length 1 are given by all permutations of:

## Related polychora[edit | edit source]

The great tesseractitesseractihexadecachoron is the colonel of a regiment with a total of 8 uniform and 6 scaliform members. Of these members, 7 have full tesseractic symmetry, namely gittith, quidpith, picnut, gittifcoth, gahfipto, gnappoth, and gnipto. The eighth member, gaquipadah, has square duoprism symmetry, as do the 6 scaliform members. The compound octagrammic diorthoprism can be edge-inscribed in this polychoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 12: Podiumverts" (#484).

- Klitzing, Richard. "gittith".