# Small ditetrahedronary dishecatonicosachoron

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Small ditetrahedronary dishecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Siddatady |

Coxeter diagram | o3o3o5/3x5*b () |

Elements | |

Cells | 120 dodecahedra, 120 ditrigonary dodecadodecahedra |

Faces | 1440 pentagons, 720 pentagrams |

Edges | 3600 |

Vertices | 600 |

Vertex figure | Hypertruncated tetrahedron, edge lengths (1+√5)/2 (triangle edges) and (√5–1)/2 (other edges) |

Edge figure | (doe 5 ditdid 5/2 ditdid 5) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Ditdid–5/2–ditdid: 144° |

Ditdid–5–doe: 36° | |

Central density | 5 |

Number of external pieces | 11160 |

Level of complexity | 31 |

Related polytopes | |

Army | Hi |

Regiment | Sidtaxhi |

Conjugate | Grand ditetrahedronary dishecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | –1080 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **small ditetrahedronary dishecatonicosachoron**, or **siddatady**, is a nonconvex uniform polychoron that consists of 120 regular dodecahedra and 120 ditrigonary dodecadodecahedra. 4 ditrigonary dodecadodecahedra and 4 dodecahedra 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" (#780).

- Klitzing, Richard. "siddatady".