# Small ditrigonary hexacosihecatonicosachoron

Small ditrigonary hexacosihecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sidtixhi |

Coxeter diagram | x3o3o3o5/2*b () |

Elements | |

Cells | 600 tetrahedra, 120 great icosahedra |

Faces | 2400 triangles |

Edges | 1200 |

Vertices | 120 |

Vertex figure | Small ditrigonary icosidodecahedron, edge length 1 |

Edge figure | (tet 3 gike 3)×3 |

Measures (edge length 1) | |

Circumradius | 1 |

Hypervolume | |

Dichoral angle | |

Central density | 9 |

Number of external pieces | 15840 |

Level of complexity | 51 |

Related polytopes | |

Army | Ex |

Regiment | Sishi |

Company | Sidtixhi |

Dual | Small triambic icosahedral hecatonicosachoron |

Conjugate | Great ditrigonary hexacosihecatonicosachoron |

Convex core | Truncated hexacosichoron |

Abstract & topological properties | |

Euler characteristic | 600 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **small ditrigonary hexacosihecatonicosachoron**, or **sidtixhi**, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra and 120 regular great icosahedra. 12 great icosahedra and 20 tetrahedra join at each vertex, with a small ditrigonary icosidodecahedron as the vertex figure.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small stellated hecatonicosachoron.

## Related polychora[edit | edit source]

The small ditrigonary hexacosihecatonicosachoron has the same edges as the regular small stellated hecatonicosachoron. It shares its face arrangement with the ditrigonary dishecatonicosachoron and the great ditrigonary hexacosihecatonicosachoron. Also sharing this set of faces is the dodecahedronary hexacosichoron, a uniform compound of 25 icositetrachora. Besides these three polychora, there is only one other face-transitive uniform polychoron which is not regular, namely the tesseractihemioctachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 17: Sishi Regiment" (#764).

- Klitzing, Richard. "sidtixhi".