# Great distetracontoctachoron

Great distetracontoctachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Giddic |

Coxeter diagram | x3o4o3x4/3*a () |

Elements | |

Cells | 48 octahedra, 48 quasitruncated hexahedra |

Faces | 384 triangles, 144 octagrams |

Edges | 576 |

Vertices | 144 |

Vertex figure | Square antiprism, edge lengths 1 (base) and √2–√2 (sides) |

Edge figure | oct 3 quith 8/3 quith 8/3 quith 3 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Quith–8/3–quith: 135° |

Oct–3–quith: 120° | |

Central density | 14 |

Number of external pieces | 720 |

Level of complexity | 23 |

Related polytopes | |

Army | Spic, edge length |

Regiment | Giddic |

Conjugate | Small distetracontoctachoron |

Abstract & topological properties | |

Flag count | 9216 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | No |

Nature | Tame |

The **great distetracontoctachoron**, or **giddic**, is a nonconvex uniform polychoron that consists of 48 regular octahedra and 48 quasitruncated hexahedra. 2 octahedra and 8 quasitruncated hexahedra join at each vertex.

The great distetracontoctachoron contains the vertices and edges of an octagrammic duoprism, sphenoverted tesseractitesseractihexadecachoron, and quasitruncated hexahedral prism.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a great distetracontoctachoron of edge length 1 are all permutations of:

The second set of vertices are identical to the vertices of an inscribed sphenoverted tesseractitesseractihexadecachoron.

## Related polychora[edit | edit source]

The great distetracontoctachoron is the colonel of a regiment that includes 20 members, 2 fissaries, and a compound. Among the members, 8 in total have doubled F4 symmetry, including the great distetracontoctachoron itself, the quasiprismatotetracontoctachoron, and the noble great retrotetracontoctachoron, while the 12 remaining members, and the fissaries and compound, have single F4 symmetry only.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 13: Spic and Giddic Regiments" (#532).

- Klitzing, Richard. "giddic".