# Hecatonicosihecatonicosihexacosichoron

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Hecatonicosihecatonicosihexacosichoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Hihix |

Elements | |

Cells | 600 truncated tetrahedra, 120 tuncated great icosahedra, 120 small ditrigonal dodecicosidodecahedra |

Faces | 2400 triangles, 1440 pentagrams, 2400 hexagons, 720 decagons |

Edges | 3600+3600 |

Vertices | 2400 |

Vertex figure | Inverted triangular antipodium, edge lengths (√5–1)/2 (top base), 1 (bottom base), √3 (side edges of triangles), and √(5+√5)/2 (side edges of crossed trapezoids) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Tiggy–6–tut: |

Sidditdid–3–tut: | |

Sidditdid–10–sidditdid: 72° | |

Sidditdid–5/2–tiggy: 72° | |

Central density | 81 |

Number of external pieces | 188880 |

Level of complexity | 686 |

Related polytopes | |

Army | Semi-uniform Sidpixhi |

Regiment | Sadixady |

Conjugate | Hexacosihecatonicosintercepted hecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | 1320 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Wild |

The **hecatonicosihecatonicosihexacosichoron**, or **hihix**, is a nonconvex uniform polychoron that consists of 120 truncated great icosahedra, 600 truncated tetrahedra, and 120 small ditrigonal dodecicosidodecahedra. Three truncated great icosahedra, three truncated tetrahedra, and three small ditrigonal dodecicosidodecahedra join at each vertex.

It also has 120 great stellated dodecahedra and 600 tetrahedra as pseudofacets.

## 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" (#472).