# Prismatohemidecachoron

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Prismatohemidecachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Phud |

Elements | |

Cells | 20 triangular prisms, 5 octahemioctahedra |

Faces | 40 triangles, 30 squares, 10 hexagons |

Edges | 60 |

Vertices | 20 |

Vertex figure | Inverted triangular antiprism, edge lengths 1 (bas edges), √2 (side edges of triangles), and √3 (side edges of bowties) |

Edge figure | trip 4 trip 4 trip 3 oho 6 oho 3 |

Measures (edge length 1) | |

Circumradius | 1 |

Hypervolume | |

Dichoral angles | Trip–4–trip: |

Oho–6–oho: | |

Oho–3–trip: | |

Number of external pieces | 60 |

Level of complexity | 7 |

Related polytopes | |

Army | Spid |

Regiment | Spid |

Conjugate | None |

Abstract & topological properties | |

Flag count | 1200 |

Euler characteristic | 15 |

Orientable | Yes |

Properties | |

Symmetry | A_{4}×2, order 240 |

Convex | No |

Nature | Wild |

The **prismatohemidecachoron**, or **phud**, is a nonconvex uniform polychoron that consists of 20 triangular prisms and 5 octahemioctahedra. Six triangular prisms and three octahemioctahedra join at each vertex.

It also has 10 tetrahedra 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" (#445).

- Klitzing, Richard. "phud".