# Small birhombatotetracontoctachoron

Small birhombatotetracontoctachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Sabric |

Coxeter diagram | ao3ob4bo3oa&#zc (1/2 < b:a < 2+√2) |

Elements | |

Cells | 288 tetragonal disphenoids, 384 triangular antipodiums, 144 square antiprisms, 48 cuboctahedra |

Faces | 192+384 triangles, 1152+1152 isosceles triangles, 288 squares |

Edges | 576+1152+1152 |

Vertices | 576 |

Vertex figure | Apex-truncated augmented triangular prism |

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

Edge lengths | Lacing edges (1152): |

Base edge 1 (576): 1 | |

Base edge 2 (1152): 1 | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Sabric |

Regiment | Sabric |

Dual | Small biorthotetracontoctachoron |

Abstract & topological properties | |

Flag count | 39168 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **small birhombatotetracontoctachoron** or **sabric** is a convex isogonal polychoron that consists of 48 cuboctahedra, 144 square antiprisms, 384 triangular antipodiums, and 288 tetragonal disphenoids. 1 cuboctahedron, 2 square antiprisms, 4 triangular antipodiums, and 2 tetragonal disphenoids 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 small rhombated icositetrachora. In this case, the ratio between the edges of the small rhombated icositetrachoron a3o4b3o is between b:a = 1/2 (producing the rectified small prismatotetracontoctachoron) and b:a = 2+√2 (producing the rectified tetracontoctachoron). This includes the convex hull of two uniform small rhombated icositetrachora. The lacing edges generally have length .

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.30656.

## External links[edit | edit source]

- Klitzing, Richard. "sabric".