# Disicositetratruncated disicositetrachoron

Disicositetratruncated disicositetrachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Ditdi |

Coxeter diagram | x3x4x3o4*a4/3*c () |

Elements | |

Cells | 24 truncated octahedra, 24 truncated cubes, 24 great cubicuboctahedra, 24 cuboctatruncated cuboctahedra |

Faces | 192 triangles, 144 squares, 192 hexagons, 144 octagons, 144 octagrams |

Edges | 288+576+576 |

Vertices | 576 |

Vertex figure | Isosceles trapezoidal pyramid, base edge lengths 1, √2–√2, √2, √2–√2; lateral edge lengths √3, √3, √2+√2, √2+√2 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Gocco–4–toe: 135° |

Tic–8–cotco: 135° | |

Gocco–8/3–cotco: 135° | |

Gocco–3–tic: 120° | |

Toe–6–cotco: 120° | |

Related polytopes | |

Army | Semi-uniform Grico, edge lengths (truncated cubes), 1 (sides of triangular prisms) |

Regiment | Ditdi |

Conjugate | Disicositetraquasitruncated disicositetrachoron |

Abstract & topological properties | |

Flag count | 18432 |

Euler characteristic | –144 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | No |

Nature | Tame |

The **disicositetratruncated disicositetrachoron**, or **ditdi**, is a nonconvex uniform polychoron that consists of 24 truncated octahedra, 24 truncated cubes, 24 great cubicuboctahedra, and 24 cuboctatruncated cuboctahedra. 1 truncated cube, 1 truncated octahedron, 1 great cubicuboctahedron, and 2 cuboctatruncated cuboctahedra join at each vertex.

The disicositetratruncated disicositetrachoron contains the vertices of a tesseractihexadecatruncated prismatotesseractihexadecachoron.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a disicositetratruncated disicositetrachoron of edge length 1 are given by all permutations of:

The second set of vertices are identical to the vertices of an inscribed tesseractihexadecatruncated prismatotesseractihexadecachoron.

## Related polychora[edit | edit source]

The disicositetratruncated disicositetrachoron is the colonel of a 3-member regiment that also includes the great tetrisicositetrachoron and great rhombic trisicositetrachoron.

# External links=[edit | edit source]

- Bowers, Jonathan. "Category 10: Prismatorhombates" (#412).

- Klitzing, Richard. "ditdi".