# Great biprismatorhombatotetracontoctachoron

Great biprismatorhombatotetracontoctachoron | |
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Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Gabiparc |

Coxeter diagram | ac3bo4ob3ca&#zd (c > a+2b) |

Elements | |

Cells | 576 wedges, 288 rectangular trapezoprisms, 144 square antiprisms, 192 ditrigonal prisms, 48 truncated octahedra |

Faces | 1152 isosceles triangles, 288 squares, 576+576 rectangles, 1152 isosceles trapezoids, 384 ditrigons |

Edges | 576+1152+1152+1152 |

Vertices | 1152 |

Vertex figure | Paratriakis isosceles trapezoidal pyramid |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Gabiparc |

Regiment | Gabiparc |

Dual | Great bicrystallorthotetracontoctachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **great biprismatorhombatotetracontoctachoron** or **gabiparc** is a convex isogonal polychoron that consists of 48 truncated tetrahedra, 192 ditrigonal prisms, 144 square antiprisms, 288 rectangular trapezoprisms, and 576 wedges. 1 truncated octahedron, 2 ditrigonal prisms, 1 square antiprism, 2 rectangular trapezoprisms, and 3 wedges join at each vertex.

[It is one of a total of five distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite prismatorhombated icositetrachora. In this case, if the prismatorhombated icositetrachora are of the form a3b4o3c, then c must be greater than a+2b (producing the truncated small prismatotetracontoctachoron in the limiting case). The lacing edges generally have length .