# Small hexacosifaceted hexacosidishecatonicosachoron

The **small hexacosifaceted hexacosidishecatonicosachoron**, or **six fixady**, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra, 600 truncated tetrahedra, and 120 small icosicosidodecahedra. One great stellated dodecahedron, three truncated tetrahedra, and three small icosicosidodecahedra join at each vertex.

Small hexacosifaceted hexacosidishecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Six fixady |

Elements | |

Cells | 600 truncated tetrahedra, 120 great stellated dodecahedra, 120 small icosicosidodecahedra |

Faces | 2400 triangles, 1440 pentagrams, 2400 hexagons |

Edges | 3600+3600 |

Vertices | 2400 |

Vertex figure | Triangular hemiantipodium, edge lengths (√5–1)/2 (top triangle), 1 (base pseudo-triangle), and √3 (sides) |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Siid–6–tut: |

Siid–5/2–gissid: 72° | |

Siid–3–tut: | |

Number of external pieces | 294120 |

Level of complexity | 925 |

Related polytopes | |

Army | Semi-uniform Sidpixhi |

Regiment | Sadixady |

Conjugate | Great hexacosifaceted hexacosidishecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | 600 |

Orientable | No |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

It also has 120 truncated great icosahedra and 600 tetrahedra as pseudofacets.

## Gallery Edit

## Vertex coordinates Edit

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

## External links Edit

- Bowers, Jonathan. "Category 11: Antipodiumverts" (#469).