# Ditetrahedronary dishecatonicosachoron

Ditetrahedronary dishecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Dattady |

Coxeter diagram | o3o3o3x5/2*b () |

Elements | |

Cells | 120 great stellated dodecahedra, 120 small ditrigonary icosidodecahedra |

Faces | 1200 triangles, 1440 pentagrams |

Edges | 3600 |

Vertices | 600 |

Vertex figure | Semi-uniform truncated tetrahedron, edge lengths (√5–1)/2 (triangle edges) and 1 (other edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Sidtid–5/2–gissid: 144° |

Sidtid–3–sidtid: 120° | |

Central density | 9 |

Number of external pieces | 2520 |

Level of complexity | 11 |

Related polytopes | |

Army | Hi, edge length |

Regiment | Dattady |

Conjugate | Great ditetrahedronary dishecatonicosachoron |

Abstract & topological properties | |

Flag count | 43200 |

Euler characteristic | –600 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **ditetrahedronary dishecatonicosachoron**, or **dattady**, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra and 120 small ditrigonary icosidodecahedra. 4 small ditrigonary icosidodecahedra and 4 great stellated dodecahedra join at each vertex, with a variant of the truncated tetrahedron as the vertex figure.

The ditetrahedronary dishecatonicosachoron contains the vertices and edges of a hexagonal duoprism, rhombidodecadodecahedral prism, and decachoron.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a ditetrahedronary dishecatonicosachoron of edge length 1, centered at the origin, are given by all permutations of:

together with all the even permutations of:

## Related polychora[edit | edit source]

The ditetrahedronary dishecatonicosachoron is the colonel of a regiment with 37 members, plus four fissaries and two compounds, as well as a number of scaliform members.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 18: Ditetrahedrals" (#815).

- Bowers, Jonathan. "How to Make Dattady".

- Klitzing, Richard. "dattady".