# Small omnisnub bitetrahedral tetracontoctachoron

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Small omnisnub bitetrahedral tetracontoctachoron | |
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File:Small omnisnub bitetrahedral tetracontoctachoron.png | |

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Sosbitic |

Elements | |

Cells | 144 rhombic disphenoids, 288+288 phyllic disphenoids, 576 irregular tetrahedra, 192+192 chiral triangular antipodiums, 48 snub tetrahedra |

Faces | 192+192+192 triangles, 576+576+576+576+576+576+576 scalene triangles |

Edges | 288+288+288+288+576+576+576+576 |

Vertices | 576 |

Vertex figure | 12-vertex polyhedron with 1 pentagon, 4 tetragons, and 9 triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Sosbitic |

Regiment | Sosbitic |

Dual | Small dodecahedral pentacosiheptacontahexachoron |

Abstract & topological properties | |

Flag count | 55296 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}●B_{3}, order 576 |

Convex | Yes |

Nature | Tame |

The **small omnisnub bitetrahedral tetracontoctachoron** or **sosbitic** is a convex isogonal polychoron that consists of 48 snub tetrahedra, 384 chiral triangular antipodiums of two kinds, 144 rhombic disphenoids, 576 phyllic disphenoids of two kinds, and 576 irregular tetrahedra. 1 snub tetrahedron, 4 triangular antipodiums, 1 rhombic disphenoid, 4 phyllic disphenoids, and 4 irregular tetrahedra join at each vertex. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:*a* ≈ 1:1.50346, where *a* is the second-largest real root of 3577a^{16}-23884a^{14}+55794a^{12}-54896a^{10}+23031a^{8}-3672a^{6}+358a^{4}-20a^{2}+1.