# Small ditrigonal hecatonicosihexacosihecatonicosachoron

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Small ditrigonal hecatonicosihexacosihecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Sidthixhi |

Coxeter diagram | o3o3x5x5/3*b () |

Elements | |

Cells | 600 tetrahedra, 120 great stellated dodecahedra, 120 small ditrigonal dodecicosidodecahedra |

Faces | 2400 triangles, 1440 pentagrams, 720 decagons |

Edges | 3600+3600 |

Vertices | 2400 |

Vertex figure | Crossed triangular frustum, edge lengths 1 (large base), (√5–1)/2 (small base), and √(5+√5)/2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Sidditdid–3–tet: |

Sidditdid–10–sidditdid: 72° | |

Sidditdid–5/2–gissid: 72° | |

Number of external pieces | 51120 |

Level of complexity | 214 |

Related polytopes | |

Army | Semi-uniform Sidpixhi |

Regiment | Sadixady |

Conjugate | Great ditrigonal hecatonicosihexacosihecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | –1080 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **small ditrigonal hecatonicosihexacosihecatonicosachoron**, or **sidthixhi**, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 great stellated dodecahedra, and 120 small ditrigonal dodecicosidodecahedra. 1 tetrahedron, 1 great stellated dodecahedron, and 3 small ditrigonal dodecicosidodecahedra join at each vertex.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 11: Antipodiumverts" (#471).

- Klitzing, Richard. "sidthixhi".