# Small dodecahedral pentacosiheptacontahexachoron

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

Small dodecahedral pentacosiheptacontahexachoron | |
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Rank | 4 |

Type | Isotopic |

Elements | |

Cells | 576 14-vertex dodecahedra |

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

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

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

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

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Small omnisnub bitetrahedral tetracontoctachoron |

Abstract & topological properties | |

Flag count | 55296 |

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 hexagon, 2 pentagons, 5 tetragons, and 4 triangles for faces.