# Medial biprismatorhombatotetracontoctachoron

Medial biprismatorhombatotetracontoctachoron | |
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Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Mabiparc |

Coxeter diagram | ac3bo4ob3ca&#zd (a+(2-√2)b/2 < c < a+2b) |

Elements | |

Cells | 192 triangular prisms, 288 rectangular trapezoprisms, 144 square antiprisms, 384 triangular cupolas, 48 truncated octahedra |

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

Edges | 576+1152+1152+1152 |

Vertices | 1152 |

Vertex figure | 7-vertex polyhedron with 2 trapezoids and 6 triangles |

Measures | |

Central density | 1 |

Related polytopes | |

Army | Mabiparc |

Regiment | Mabiparc |

Dual | Medial bicrystallorthotetracontoctachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **medial biprismatorhombatotetracontoctachoron** or **mabiparc** is a convex isogonal polychoron that consists of 48 truncated octahedra, 144 square antiprisms, 288 rectangular trapezoprisms, 192 triangular prisms, and 384 triangular cupolas. 1 truncated octahedron, 1 square antiprism, 2 rectangular trapezoprisms, 1 triangular prism, and 3 triangular cupolas join 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 between (producing the transitional biprismatorhombatotetracontoctachoron) and a+2b (producing the truncated small prismatotetracontoctachoron). The lacing edges generally have length .