# Bitruncatotetrahedral tetracontoctachoron

The **bitruncatotetrahedral tetracontoctachoron** or **bitutic** is a convex isogonal polychoron that consists of 48 truncated tetrahedra, 192 chiral triangular antipodiums, 192 triangular-ditrigonal gyrowedges, 144 rhombic disphenoids, and 576 phyllic disphenoids of two kinds. 1 truncated tetrahedron, 2 triangular antipodiums, 3 triangular-ditrigonal gyrowedges, 1 rhombic disphenoid, and 4 phyllic disphenoids join at each vertex. However, it cannot be made scaliform.

Bitruncatotetrahedral tetracontoctachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Bitutic |

Elements | |

Cells | 144 rhombic disphenoids, 288+288 phyllic disphenoids, 48 truncated tetrahedra, 192 chiral triangular antipodiums, 192 triangular-ditrigonal gyrowedges |

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

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 | Bitutic |

Regiment | Bitutic |

Dual | 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 |