# Small hecatonicosintercepted hecatonicosachoron

(Redirected from Shinhi)

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Small hecatonicosintercepted hecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Shinhi |

Elements | |

Cells | 120 icosidodecahedra, 120 truncated dodecahedra |

Faces | 2400 triangles, 720 pentagons, 720 decagons |

Edges | 3600 |

Vertices | 1200 |

Vertex figure | Triangular toroprism, edge lengths 1 (base edges), (1+√5)/2 (side edges of rectangles), and √(5+√5)/2 (side edges of triangles) |

Edge figure | id 5 id 3 tid 10 tid 10 tid 3 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Id–5–id: 144° |

Id–3–tid: 120° | |

Tid–10–tid: 60° | |

Number of pieces | 2520 |

Level of complexity | 6 |

Related polytopes | |

Army | Rahi |

Regiment | Rahi |

Conjugate | Great hecatonicosintercepted hecatonicosachoron |

Convex core | Hecatonicosachoron |

Abstract properties | |

Euler characteristic | 1200 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Wild |

The **small hecatonicosintercepted hecatonicosachoron**, or **shinhi**, is a nonconvex uniform polychoron that consists of 120 icosidodecahedra and 120 truncated dodecahedra. 3 icosidodecahedra and 6 truncated dodecahedra join at each vertex.

It is wild because it has icosidodecahedra intercepted by decagons.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 3: Triangular Rectates" (#50).

- Klitzing, Richard. "shinhi".