# Small retroditetrahedronary hexacosidishecatonicosachoron

Jump to navigation
Jump to search

Small retroditetrahedronary hexacosidishecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sirdtaxady |

Coxeter diagram | x3o3/2o3o5*a () |

Elements | |

Cells | 600 tetrahedra, 120 dodecahedra, 120 icosidodecahedra |

Faces | 2400 triangles, 1440 pentagons |

Edges | 3600 |

Vertices | 600 |

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

Edge figure | (tet 3 id 5 doe 5 id 3) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Id–3–tet: |

Doe–5–id: 72° | |

Central density | 14 |

Number of external pieces | 161280 |

Level of complexity | 316 |

Related polytopes | |

Army | Hi |

Regiment | Sidtaxhi |

Company | Sidtaxady |

Conjugate | Grand ditetrahedronary hexacosidishecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **small retroditetrahedronary hexacosidishecatonicosachoron**, or **sirdtaxady**, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, and 120 icosidodecahedra. 4 dodecahedra, 4 tetrahedra, and 6 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" (#782).

- Klitzing, Richard. "sirdtaxady".