# Pseudorhombic prismatopentachoron

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Pseudorhombic prismatopentachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Pirpop |

Elements | |

Cells | 10 triangular prisms, 10 hexagonal prisms, 5 truncated tetrahedra |

Faces | 20 triangles, 15+30 squares, 20 hexagons |

Edges | 30+60 |

Vertices | 30 |

Vertex figure | Isosceles triangular retroprism, edge lengths 1 (2), √2 (6), and √3 (4) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Tut–3–trip: |

Tut–6–hip: | |

Trip–4–hip: | |

Hip–4–hip: | |

Related polytopes | |

Army | Srip |

Regiment | Srip |

Conjugate | None |

Convex core | Pentachoron |

Abstract & topological properties | |

Flag count | 1440 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{4}, order 120 |

Convex | No |

Nature | Tame |

The **pseudorhombic prismatopentachoron**, or **pirpop**, is a nonconvex uniform polychoron that consists of 5 truncated tetrahedra, 10 triangular prisms, and 10 hexagonal prisms. 2 truncated tetrahedra, 2 triangular prisms and 4 hexagonal prisms join at each vertex.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 6: Sphenoverts" (#136).

- Klitzing, Richard. "pirpop".