# Small pentagrammal antiprismatoverted dishecatonicosachoron

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Small pentagrammal antiprismatoverted dishecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Spapivady |

Coxeter diagram | (x5o5/2o5x5/3*a)/2 (/2) |

Elements | |

Cells | |

Faces | |

Edges | 3600 |

Vertices | 720 |

Vertex figure | Pentagrammic antiprism, edge lengths (1+√5)/2 (base) and √(5–√5)/2 (side) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angle | Quit sissid–10/3–quit sissid: 144° Gad–5–quit sissid: 108° |

Central density | 54 |

Number of external pieces | 32640 |

Level of complexity | 76 |

Related polytopes | |

Army | Rox |

Regiment | Ragishi |

Conjugate | Great pentagonal retroprismatoverted dishecatonicosachoron |

Convex core | Hecatonicosachoron |

Abstract & topological properties | |

Flag count | 57600 |

Euler characteristic | –960 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Flag orbits | 4 |

Convex | No |

Nature | Tame |

The **small pentagrammal antiprismatoverted dishecatonicosachoron**, or **spapivady**, is a nonconvex uniform polychoron that consists of 120 great dodecahedra and 120 quasitruncated small stellated dodecahedra. 2 great dodecahedra and 10 quasitruncated small stellated dodecahedra join at each vertex.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices are the same as those of its regiment colonel, the rectified great stellated hecatonicosachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#105).

- Klitzing, Richard. "spapivady".