# Pentagonal triswirlprism

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Pentagonal triswirlprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 150 phyllic disphenoids, 30 pentagonal gyroprisms |

Faces | 300 scalene triangles, 150 isosceles triangles, 30 pentagons |

Edges | 75+150+150 |

Vertices | 75 |

Vertex figure | 10-vertex polyhedron with 4 tetragons and 8 triangles |

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

Edge lengths | Short side edges (75): |

Long side edges (150): | |

Edges of pentagons (150): 1 | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Dual | Pentagonal triswirltegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | (I_{2}(15)≀S_{2})+/3, order 300 |

Convex | Yes |

Nature | Tame |

The **pentagonal triswirlprism** is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 30 pentagonal gyroprisms and 150 phyllic disphenoids. 4 pentagonal gyroprisms and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the pentadecagonal duoprism. It is the third in an infinite family of isogonal pentagonal dihedral swirlchora.

The ratio between the longest and shortest edges is 1: ≈ 1:1.99906.