# Small retroinverted ditetrahedronary trishecatonicosachoron

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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 |

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.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

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

- Klitzing, Richard. "sridtathi".