# Biprismatotetracontoctachoron

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Biprismatotetracontoctachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Bipec |

Coxeter diagram | ab3oo4oo3ba&#zc |

Elements | |

Cells | 48 octahedra, 192 triangular prisms, 288 rectangular trapezoprisms |

Faces | 384 triangles, 576 isosceles trapezoids, 576 rectangles |

Edges | 144+576+576 |

Vertices | 288 |

Vertex figure | Triakis square pyramid |

Measures (for variant with trapezoids with 3 equal edges) | |

Edge lengths | Short base edges (576): 1 |

Lacing edges (144): 1 | |

Long base edges (576): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Bipec |

Regiment | Bipec |

Dual | Bicrystallotetracontoctachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **biprismatotetracontoctachoron** or **bipec** is a convex isogonal polychoron that consists of 48 octahedra, 288 rectangular trapezoprisms and 192 triangular prisms. 1 octahedron, 4 triangular prisms, and 4 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two opposite small disprismatoicositetricositetrachora (that is, variants of the small prismatotetracontoctachoron with F_{4} symmetry).

If the small disprismatoicositetricositetrachora have edge lengths a and b, the lacing edges between then have length .

Using the ratio method, the lowest possible ratio between the longest and shortest edges is .

## External links[edit | edit source]

- Klitzing, Richard. "bipec".