# Small retroinverted ditetrahedronary trishecatonicosachoron

The **small retroinverted ditetrahedronary trishecatonicosachoron**, or **sridtathi**, is a nonconvex uniform polychoron that consists of 120 small ditrigonary icosidodecahedra, 120 dodecahedra, and 120 icosidodecahedra. Four small ditrigonary icosidodecahedra, four dodecahedra, and six icosidodecahedra join at each vertex.

Small retroinverted ditetrahedronary trishecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Sridtathi |

Elements | |

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

Faces | 2400 triangles, 1440 pentagons, 720 pentagrams |

Edges | 3600 |

Vertices | 600 |

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

Edge figure | (doe 5 id 3 sidtid 5/2 sidtid 3 id 5) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

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

Sidtid–3–id: 120° | |

Doe–5–id: 72° | |

Number of external pieces | 7320 |

Level of complexity | 17 |

Related polytopes | |

Army | Hi, edge length |

Regiment | Sidtaxhi |

Conjugate | Grand inverted ditetrahedronary trishecatonicosachoron |

Abstract & topological properties | |

Flag count | 72000 |

Euler characteristic | 1200 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Wild |

## Vertex coordinates edit

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

## External links edit

- Bowers, Jonathan. "Category 18: Ditetrahedrals" (#784).

- Klitzing, Richard. "sridtathi".