# Antipodial biomnisnub tetracontoctachoron

The **antipodial biomnisnub tetracontoctachoron** or **apbosc** is a convex isogonal polychoron that consists of 48 snub cubes, 144 square gyroprisms, 192 triangular gyroprisms, 384 chiral triangular antipodiums, 288 tetragonal disphenoids, 576 phyllic disphenoids, and 2304 irregular tetrahedra of two kinds. 1 snub cube, 1 square gyroprism, 1 triangular gyroprism, 2 triangular antipodiums, 1 tetragonal disphenoid, 2 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It is one of a total of 8 polychora that can be formed as the convex hull of 2 snub icositetrachora.

Antipodial biomnisnub tetracontoctachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Apbosc |

Elements | |

Cells | 1152+1152 irregular tetrahedra, 576 phyllic disphenoids, 288 rhombic disphenoids, 384 chiral triangular antipodiums, 192 triangular gyroprisms, 144 square gyroprisms, 48 snub cubes |

Faces | 1152+1152+1152+1152+1152+1152+1152+1152 scalene triangles, 384+384 triangles, 288 squares |

Edges | 576+576+576+576+576+1152+1152+1152+1152 |

Vertices | 1152 |

Vertex figure | 13-vertex polyhedron with 1 pentagon, 4 tetragons, and 11 triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Apbosc |

Regiment | Apbosc |

Dual | Tridecahedral chiliahecatonpentacontadichoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | (F_{4}×2)+, order 1152 |

Convex | Yes |

Nature | Tame |