# Square tetraswirlprism

Square tetraswirlprism | |
---|---|

File:Square tetraswirlprism.png | |

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 128 phyllic disphenoids, 64 rhombic disphenoids, 32 square gyroprisms |

Faces | 256+256 scalene triangles, 32 squares |

Edges | 64+64+128+128 |

Vertices | 64 |

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

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

Edge lengths | Short side edges (64): |

Medium side edges (64): | |

Long side edges (128): | |

Edges of squares (128): 1 | |

Circumradius | 1 |

Central density | 1 |

Related polytopes | |

Dual | Square tetraswirltegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | (I_{2}(16)≀S_{2})+/4, order 256 |

Convex | Yes |

Nature | Tame |

The **square tetraswirlprism** is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 32 square gyroprisms, 64 rhombic disphenoids, and 128 phyllic disphenoids. 4 square gyroprisms, 4 rhombic disphenoids and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the hexadecagonal duoprism. It is the fourth in an infinite family of isogonal square dihedral swirlchora and also the seventh in an infinite family of isogonal digonal prismatic swirlchora, the other being the digonal double octaswirlprism.

The ratio between the longest and shortest edges is 1: ≈ 1:2.56292.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a square tetraswirlprism constructed as the convex hull of four 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 22.5 degrees),_{1}*S*×_{3}*S*(_{3}*S*rotated 45 degrees),_{1}*S*×_{4}*S*(_{4}*S*rotated 67.5 degrees)._{1}