# Small biprismatorhombatotetracontoctachoron

Small biprismatorhombatotetracontoctachoron | |
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Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Sabiparc |

Coxeter diagram | ac3bo4ob3ca&#zd (c < a+(2-√2)b/2 |

Elements | |

Cells | 192 triangular prisms, 576 wedges, 288 rectangular trapezoprisms, 144 square antiprisms, 48 small rhombicuboctahedra |

Faces | 384 triangles, 1152 isosceles triangles, 288 squares, 576+576 rectangles, 1152 isosceles trapezoids |

Edges | 576+1152+1152+1152 |

Vertices | 1152 |

Vertex figure | Triangular-isosceles trapezoidal wedge |

Measures (based on two prismatorhombated icositetrachora of edge length 1) | |

Edge lengths | Lacing edges (1152): |

Remaining edges (576+1152+1152): 1 | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Sabiparc |

Regiment | Sabiparc |

Dual | Small bicrystallorthotetracontoctachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **small biprismatorhombatotetracontoctachoron** or **sabiparc** is a convex isogonal polychoron that consists of 48 small rhombicuboctahedra, 144 square antiprisms, 288 rectangular trapezoprisms, 192 triangular prisms, and 576 wedges. 1 small rhombicuboctahedron, 1 square antiprism, 2 rectangular trapezoprisms, 1 triangular prism, and 3 wedges 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 prismatorhombated icositetrachora. In this case, if the prismatorhombated icositetrachora are of the form a3b4o3c, then c must be less than (producing the transitional biprismatorhombatotetracontoctachoron in the limiting case). This includes the convex hull of two uniform prismatorhombated icositetrachora. The lacing edges generally have length .

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.39422.