# Spinoprismatodispentachoron

The **spinoprismatodispentachoron**, or **nipdip**, is a nonconvex uniform polychoron that consists of 5 tetrahedra, 10 triangular prisms, and 5 cubohemioctahedra. One tetrahedron, three triangular prisms, and three cubohemioctahedra join at each vertex.

Spinoprismatodispentachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Nipdip |

Elements | |

Cells | 5 tetrahedra, 10 triangular prisms, 5 cubohemioctahedra |

Faces | 20 triangles, 30 squares, 10 hexagons |

Edges | 30+30 |

Vertices | 20 |

Vertex figure | Triangular crown, edge lengths 1 (top triangle), √2 (side edges of triangles), and √3 (edges joining butterflies) |

Measures (edge length 1) | |

Circumradius | 1 |

Dichoral angles | Tet–3–trip: |

Cho–6–cho: | |

Cho–4–trip: | |

Number of external pieces | 45 |

Level of complexity | 12 |

Related polytopes | |

Army | Spid |

Regiment | Spid |

Conjugate | None |

Abstract & topological properties | |

Flag count | 960 |

Euler characteristic | 0 |

Orientable | No |

Properties | |

Symmetry | A_{4}, order 120 |

Convex | No |

Nature | Wild |

## Gallery edit

## Vertex coordinates edit

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

## External links edit

- Bowers, Jonathan. "Category 11: Antipodiumverts" (#446).

- Klitzing, Richard. "nipdip".