# Dodecafold icosidodecaswirlchoron

The **dodecafold icosidodecaswirlchoron** is an isogonal polychoron with 240 triangular gyroprisms, 2160 phyllic disphenoids of three kinds, and 360 vertices. 4 triangular gyroprisms and 24 phyllic disphenoids join at each vertex. It is the third in an infinite family of isogonal icosidodecahedral swirlchora.

Dodecafold icosidodecaswirlchoron | |
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File:Dodecafold icosidodecaswirlchoron.png | |

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 720+720+720 phyllic disphenoids, 240 triangular gyroprisms |

Faces | 1440+1440+1440 scalene triangles, 720 isosceles triangles, 240 triangles |

Edges | 360+720+720+720+720 |

Vertices | 360 |

Vertex figure | Polyhedron with 4 tetragons and 24 triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Rhombitriacontaswirlic triacosihexecontachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}●I_{2}(12), order 1440 |

Convex | Yes |

Nature | Tame |

The ratio between the longest and shortest edges is 1: ≈ 1:1.96681.