# Prismatopentahemidecachoron

(Redirected from Piphid)

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Prismatopentahemidecachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Piphid |

Coxeter diagram | |

Elements | |

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

Faces | 20+20 triangles, 30 squares |

Edges | 30+30 |

Vertices | 20 |

Vertex figure | Triangular cuploid, edge lengths 1 (top triangle and based pseudo-triangle) and √2 (sides) |

Measures (edge length 1) | |

Circumradius | 1 |

Dichoral angles | Tet–3–co: |

Co–4–trip: | |

Co–3–trip: | |

Number of external pieces | 85 |

Level of complexity | 20 |

Related polytopes | |

Army | Spid |

Regiment | Spid |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 10 |

Orientable | No |

Properties | |

Symmetry | A_{4}, order 120 |

Convex | No |

Nature | Tame |

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

It also has 5 tetrahedra and 10 triangular prisms as pseudofacets.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 11: Antipodiumverts" (#443).

- Klitzing, Richard. "piphid".