# Prismatic transitional biomnitruncatotetracontoctachoron

Prismatic transitional biomnitruncatotetracontoctachoron | |
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File:Prismatic transitional biomnitruncatotetracontoctachoron.png | |

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Petbotic |

Coxeter diagram | ad3bc4cb3da&#ze (d = a+b/2-c/2) |

Elements | |

Cells | 144 ditetragonal trapezoprisms, 192 orthoaligned truncated triangular prisms, 48 great rhombicuboctahedra |

Faces | 1152 isosceles trapezoids, 576 rectangles, 384 ditrigons, 288+288 ditetragons |

Edges | 1152+1152+1152+1152 |

Vertices | 2304 |

Vertex figure | Irregular tetrahedron |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Prismatic transitional intersected biomnistellatotetracontoctachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **prismatic transitional biomnitruncatotetracontoctachoron** or **petbotic** is a convex isogonal polychoron that consists of 48 great rhombicuboctahedra, 144 ditetragonal trapezoprisms, and 192 orthoaligned truncated triangular prisms. 1 reat rhombicuboctahedron, 1 ditetragnal trapezoprism, and 2 orthoaligned truncated triangular prisms join at each vertex.

It is one of a total of four distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite great disprismatoicositetricositetrachora (that is, variants of the great prismatotetracontoctachoron with single F4 symmetry). If the great disprismatoicositetricositetrachora are of the form a3b4c3d, then this form occurs when the ditrigonal prisms a c3d and a3b d have the same circumradius, which happens if d = a+b/2-c/2. The lacing edges generally have length .

This polychoron can be alternated into a prismatic transitional omnisnub bitetracontoctachoron, which is also nonuniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.70711.