# Great birhombatotetracontoctachoron

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Great birhombatotetracontoctachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Gabric |

Coxeter diagram | ao3ob4bo3oa&#zc (b:a > 2+√2) |

Elements | |

Cells | 288 tetragonal disphenoids, 576 rectangular pyramids, 144 square antiprisms, 48 small rhombicuboctahedra |

Faces | 192 triangles, 1152+1152 isosceles triangles, 288 squares, 576 rectangles |

Edges | 576+1152+1152 |

Vertices | 576 |

Vertex figure | Laterowedged wedge |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Gabric |

Regiment | Gabric |

Dual | Great biorthotetracontoctachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **great birhombatotetracontoctachoron** or **gabric** is a convex isogonal polychoron that consists of 48 small rhombicuboctahedra, 144 square antiprisms, 576 rectangular pyramids and 288 tetragonal disphenoids. 2 small rhombicuboctahedra, 2 square antiprisms, 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, the ratio between the edges of the small rhombated icositetrachoron a3o4b3o is greater than b:a = (which produces the rectified tetracontoctachoron in the limiting case). The lacing edges generally have length .

## External links[edit | edit source]

- Klitzing, Richard. "gabric".