# Pentagonal tetraswirlprism

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Pentagonal tetraswirlprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 200 phyllic disphenoids, 100 rhombic disphenoids, 40 pentagonal gyroprisms |

Faces | 400+400 scalene triangles, 40 pentagons |

Edges | 100+100+200+200 |

Vertices | 100 |

Vertex figure | 12-vertex polyhedron with 4 tetragons and 12 triangles |

Measures (based on pentagonal duoprisms of edge length 1) | |

Edge lengths | Short side edges (100): |

Medium side edges (100): | |

Long side edges (200): | |

Edges of pentagons (200): 1 | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Dual | Pentagonal tetraswirltegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | (I_{2}(20)≀S_{2})+/4, order 400 |

Convex | Yes |

Nature | Tame |

The **pentagonal tetraswirlprism** is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 40 pentagonal gyroprisms, 100 rhombic disphenoids, and 200 phyllic disphenoids. 4 pentagonal gyroprisms, 4 rhombic disphenoids, and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the icosagonal duoprism. It is the fourth in an infinite family of isogonal pentagonal dihedral swirlchora.

The ratio between the longest and shortest edges is 1: ≈ 1:2.65688.