# Cubiswirlic hecatonhexacontoctachoron

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Cubiswirlic hecatonhexacontoctachoron | |
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Rank | 4 |

Type | Isotopic |

Elements | |

Cells | 168 32-vertex octadecahedra |

Faces | 672 kites, 672 mirror-symmetric pentagons, 168 square-symmetric dodecagons |

Edges | 672+672+1344 |

Vertices | 672+672 |

Vertex figure | 672+672 phyllic disphenoids |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Icosioctafold octaswirlchoron |

Abstract & topological properties | |

Flag count | 32256 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}●I_{2}(28), order 1344 |

Flag orbits | 24 |

Convex | Yes |

Nature | Tame |

The **cubiswirlic hecatonhexacontoctachoron**, also known as the **cubeswirl 168**, is an isotopic polychoron with 168 identical cells. It is the seventh in an infinite family of isochoric cubic swirlchora.

Each cell of this polychoron has chiral square prismatic symmetry, with 2 square-symmetric dodecagons, 8 mirror-symmetric pentagons, and 8 kites for faces.