# Small tetradecahedral pentacosiheptacontahexachoron

The **small tetradecahedral pentacosiheptacontahexachoron** is a convex isochoric polychoron with 576 identical cells. It can be obtained as the dual of the small disphenoidal omnisnub bitetrahedral tetracontoctachoron.

Small tetradecahedral pentacosiheptacontahexachoron | |
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Rank | 4 |

Type | Isotopic |

Elements | |

Cells | 576 20-vertex tetradecahedra |

Faces | 576 scalene triangles, 288+288 kites, 576+576 irregular tetragons, 576+576 irregular pentagons, 288 mirror-symmetric hexagons, 288 mirror-symmetric octagons |

Edges | 192+192+576+576+576+576+576+576+576+576+576+576 |

Vertices | 48+144+192+288+288+576+576+576 |

Vertex figure | 48 tetartoids, 192 chiral triangular antitegums, 144 rhombic disphenoids, 288+288 phyllic disphenoids, 576+576+576 irregular tetrahedra |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Small disphenoidal omnisnub bitetrahedral tetracontoctachoron |

Abstract & topological properties | |

Flag count | 73728 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}●B_{3}, order 576 |

Convex | Yes |

Nature | Tame |

Each cell of this polychoron is completely asymmetric, with 1 octagon, 1 hexagon, 4 pentagons, 6 tetragons, and 2 triangles for faces.