# Medial birhombatotetracontoctachoron

Medial birhombatotetracontoctachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Mabric |

Coxeter diagram | ao3ob4bo3oa&#zc (b:a < 1/2) |

Elements | |

Cells | 288 tetragonal disphenoids, 576 rectangular pyramids, 192 triangular prisms, 144 square antiprisms, 48 cuboctahedra |

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

Edges | 576+1152+1152 |

Vertices | 576 |

Vertex figure | Paratetrakis rectangular frustum |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Mabric |

Regiment | Mabric |

Dual | Medial biorthotetracontoctachoron |

Abstract & topological properties | |

Flag count | 46080 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **medial birhombatotetracontoctachoron** or **mabric** is a convex isogonal polychoron that consists of 48 cuboctahedra, 144 square antiprisms, 192 triangular prisms, 576 rectangular pyramids, and 288 tetragonal disphenoids 1 cuboctahedron, 2 square antiprisms, 2 triangular prisms, 5 rectangular pyramids, and 2 tetragonal disphenoids 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 small rhombated icositetrachora. In this case, the4 ratio between the edges of the small rhombated pentachoron a3o4b3o is less than b:a = 1/2 (which produces the rectified small prismatotetracontoctachoron in the limiting case). The lacing edges generally have length .

## External links[edit | edit source]

- Klitzing, Richard. "mabric".