# Triangular transitional omnisnub bitetrahedral tetracontoctachoron

The **triangular transitional omnisnub bitetrahedral tetracontoctachoron** or **titosbetic** is a convex isogonal polychoron that consists of 48 snub tetrahedra, 192 gyrated tridiminished icosahedra, 144 rhombic disphenoids, 288 phyllic disphenoids, and 576 irregular tetrahedra. 1 snub tetrahedron, 3 gyrated tridiminished icosahedra, 1 rhombic disphenoid, 2 phyllic disphenoids, and 4 irregular tetrahedra join at each vertex. However, it cannot be made scaliform.

Triangular transitional omnisnub bitetrahedral tetracontoctachoron | |
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Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Titosbetic |

Elements | |

Cells | 144 rhombic disphenoids, 288 phyllic disphenoids, 576 irregular tetrahedra, 48 snub tetrahedra, 192 gyrated tridiminished icosahedra |

Faces | 192+192 triangles, 576+576+576+576+576 scalene triangles, 288 isosceles trapezoids |

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

Vertices | 576 |

Vertex figure | 10-vertex polyhedron |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Titosbetic |

Regiment | Titosbetic |

Dual | Transitional intersected decahedral pentacosiheptacontahexachoron |

Abstract & topological properties | |

Flag count | 43776 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}●B_{3}, order 576 |

Convex | Yes |

Nature | Tame |