# Retroditetrahedronary trishecatonicosachoron

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Retroditetrahedronary trishecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Radatathi |

Coxeter diagram | o3o3o5x5/3*a () |

Elements | |

Cells | 120 dodecahedra, 120 great stellated dodecahedra, 120 dodecadodecahedra |

Faces | 1440 pentagons, 1440 pentagrams |

Edges | 3600 |

Vertices | 600 |

Vertex figure | Quasirhombitetratetrahedron, edge lengths (√5–1)/2 and (1+√5)/2 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Doe–5–did: 144° |

Gissid–5/2–did: 72° | |

Central density | 65 |

Number of external pieces | 45720 |

Level of complexity | 105 |

Related polytopes | |

Army | Hi |

Regiment | Dattady |

Company | Dattathi |

Conjugate | Retroditetrahedronary dishecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | –480 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **retroditetrahedronary trishecatonicosachoron**, or **radatathi**, is a nonconvex uniform polychoron that consists of 120 regular dodecahedra, 120 great stellated dodecahedra, and 120 dodecadodecahedra. 4 great stellated dodecahedra, 4 dodecahedra, and 6 dodecadodecahedra join at each vertex.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the ditetrahedronary dishecatonicosachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 18: Ditetrahedrals" (#819).

- Klitzing, Richard. "radatathi".