# Prismatic transitional omnisnub bitetracontoctachoron

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Prismatic transitional omnisnub bitetracontoctachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Petosbic |

Elements | |

Cells | 1152 irregular tetarhedar, 192 gyrated rectified triangular prisms, 144 square antiprisms, 48 snub cubes |

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

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

Vertices | 1152 |

Vertex figure | 9-vertex polyhedron with 2 pentagons, 2 tetragons, and 4 triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Petosbic |

Regiment | Petosbic |

Dual | Enneahedral chiliahecatonpentacontadichoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}+×2, order 1152 |

Convex | Yes |

Nature | Tame |

The **prismatic transitional omnisnub bitetracontoctachoron** or **petosbic** is a convex isogonal polychoron that consists of 48 snub cubes, 144 square antiprisms, 192 gyrated rectified triangular prisms, and 1152 irregular tetrahedra. 1 snub cube, 1 square antiprism, 2 gyrated rectified triangular prisms, and 4 irregular tetrahedra join at each vertex. It can be obtained through the process of alternating the prismatic transitional biomnitruncatotetracontoctachoron.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.57428.