# Triangular tetraswirlprism

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Triangular tetraswirlprism | |
---|---|

File:Triangular tetraswirlprism.png | |

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 36 rhombic disphenoids, 72 phyllic disphenoids, 24 triangular gyroprisms |

Faces | 144+144 scalene triangles, 24 triangles |

Edges | 36+36+72+72 |

Vertices | 36 |

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

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

Edge lengths | Short side edges (36): |

Medium side edges (36): | |

Long side edges (72): | |

Edges of triangles (72): 1 | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Dual | Triangular tetraswirltegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | (I_{2}(12)≀S_{2})+/4, order 144 |

Convex | Yes |

Nature | Tame |

The **triangular tetraswirlprism** is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 24 triangular antiprisms, 36 rhombic disphenoids, and 72 phyllic disphenoids. 4 triangular gyroprisms, 4 rhombic disphenoids, and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the dodecagonal duoprism. It is the fourth in an infinite family of isogonal triangular dihedral swirlchora.

The ratio between the longest and shortest edges is 1: ≈ 1:2.36603.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a triangular tetraswirlprism constructed as the convex hull of four triangular duoprisms of edge length 1, are given as Cartesian products of the vertices of triangle *T _{1}*:

*T*×_{1}*T*,_{1}*T*×_{2}*T*(_{2}*T*rotated 30 degrees),_{1}*T*×_{3}*T*(_{3}*T*rotated 60 degrees)._{1}*T*×_{4}*T*(_{4}*T*rotated 90 degrees)._{1}