# Square triswirlprism

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Square triswirlprism | |
---|---|

File:Square triswirlprism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 96 phyllic disphenoids, 24 square gyroprisms |

Faces | 192 scalene triangles, 96 isosceles triangles, 24 squares |

Edges | 48+96+96 |

Vertices | 48 |

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

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

Edge lengths | Short side edges (48): |

Long side edges (96): | |

Edges of squares (96): 1 | |

Circumradius | 1 |

Central density | 1 |

Related polytopes | |

Dual | Square triswirltegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | (I_{2}(12)≀S_{2})+/3, order 192 |

Convex | Yes |

Nature | Tame |

The **square triswirlprism** is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 24 square gyroprisms and 96 phyllic disphenoids. 4 square gyroprisms and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the dodecagonal duoprism. It is the third in an infinite family of isogonal square dihedral swirlchora.

The ratio between the longest and shortest edges is 1: ≈ 1:1.93185.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a square triswirlprism constructed as the convex hull of three square duoprisms of edge length 1, are given as Cartesian products of the vertices of square *S _{1}*:

*S*×_{1}*S*,_{1}*S*×_{2}*S*(_{2}*S*rotated 30 degrees),_{1}*S*×_{3}*S*(_{3}*S*rotated 60 degrees)._{1}