# Bi-icositetrareplenished grand hexacosichoron

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Bi-icositetrareplenished grand hexacosichoron | |
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File:Bi-icositetrareplenished grand hexacosichoron.png | |

Rank | 4 |

Type | Scaliform |

Notation | |

Bowers style acronym | Birgax |

Elements | |

Cells | 48 trireplenished great icosahedra |

Faces | 48+72 triangles, 72 pentagrams |

Edges | 72+144 |

Vertices | 72 |

Vertex figure | Bi-trireplenished great icosahedron, edge lengths 1 and (√5-1)/2 |

Measures (edge length 1) | |

Circumradius | |

Central density | -1 |

Related polytopes | |

Army | Bidex |

Regiment | Birgax |

Conjugate | Bi-icositetradiminished hexacosichoron |

Abstract & topological properties | |

Flag count | 2880 |

Orientable | Yes |

Properties | |

Symmetry | (B_{3}/2)●G_{2}, order 144 |

Convex | No |

Nature | Tame |

The **bi-icositetrareplenished grand hexacosichoron**, or **birgax**, is a nonconvex noble scaliform polychoron that consists of 48 trireplenished great icosahedra. Six cells join at each vertex.

It can be formed from the grand hexacosichoron in a similar way as its conjugate, the bi-icositetradiminished hexacosichoron, can be derived from the hexacosichoron, by removing 48 great icosahedral pyramids corresponding to the vertices of 2 inscribed great icosahedra. Removing only 1 set of 24 vertices instead results in the retrosnub disicositetrachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category S3: Special Scaliforms" (#S23).

- Klitzing, Richard. "birgax".