# Small tripesic hecatonicosachoron

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Small tripesic hecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sitphi |

Coxeter diagram | (o5/2x5x5/2o)/2 (/2) |

Elements | |

Cells | 120 truncated great dodecahedra |

Faces | 720 pentagrams, 720 decagons |

Edges | 3600 |

Vertices | 600 |

Vertex figure | Compound of 3 tetragonal disphenoids, edge lengths (√5–1)/2 (base) and √(5+√5)/2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dichoral angles | Tigid–10–tigid: 108° |

Tigid–5/2–tigid: 72° | |

Related polytopes | |

Army | Hi |

Regiment | Sidtaxhi |

Conjugate | Great tripesic hecatonicosachoron |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **small tripesic hecatonicosachoron**, or **sitphi**, is a nonconvex noble fissary uniform polychoron that consists of 120 truncated great dodecahedra as cells. 12 cells join at each vertex.

It is fissary due to having a compound vertex figure, specifically a compound of three disphenoids. It shares its edges with the small ditetrahedronary hexacosihecatonicosachoron.

A double cover of this polychoron can be seen as the bitruncated grand stellated hecatonicosachoron.

## Cross sections[edit | edit source]

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 7: Bitruncates" (#F1).

- Bowers, Jonathan. "Category 18: Ditetrahedrals" (#F1).

- Klitzing, Richard. "sitphi".