# Small disphenoidal omnisnub bitetrahedral tetracontoctachoron

Small disphenoidal omnisnub bitetrahedral tetracontoctachoron | |
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Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Sidwosbitac |

Elements | |

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

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

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

Vertices | 576 |

Vertex figure | 14-vertex polyhedron with 1 pentagon, 2 tetragons, and 17 triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Sidwosbitac |

Regiment | Sidwosbitac |

Dual | Small tetradecahedral pentacosiheptacontahexachoron |

Abstract & topological properties | |

Flag count | 73728 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}●B_{3}, order 576 |

Convex | Yes |

Nature | Tame |

The **small disphenoidal omnisnub bitetrahedral tetracontoctachoron** or **sidwosbitac** is a convex isogonal polychoron that consists of 48 snub tetrahedra, 192 chiral triangular antipodiums, 144 rhombic disphenoids, 576 phyllic disphenoids of two kinds, and 1728 irregular tetrahedra of three kinds. 1 snub tetrahedron, 2 triangular antipodiums, 1 rhombic disphenoid, 4 phyllic disphenoids, and 12 irregular tetrahedra join at each vertex. However, it cannot be made uniform.