# Digonal-square tetraswirlprism

(Redirected from 16-2 double step prism)

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Digonal-square tetraswirlprism | |
---|---|

200px | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Info | |

Symmetry | I2(8)×I2(16)/8, order 64 |

Elements | |

Cells | 8 square antiprisms, 16 rhombic disphenoids, 32+32+32 phyllic disphenoids |

Faces | 8 squares, 64+64+64+64 scalene triangles |

Edges | 16+32+32+32+32+32 |

Vertices | 32 |

Central density | 1 |

Euler characteristic | 0 |

Related polytopes | |

Dual | Digonal-square tetraswirltegum |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **digonal-square tetraswirlprism**, also known as the **16-2 double step prism** or **16-6 double step prism**, is a convex isogonal polychoron that consists of 8 square antiprisms, 16 rhombic disphenoids and 96 phyllic disphenoids of three kinds obtained as a subsymmetrical faceting of the octagonal-hexadecagonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.11968.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a digonal-square tetraswirlprism, assuming that the edge length differences are minimized, are given as Cartesian products of the vertices of square *S _{1}* and digon

*D*with length ratio 1:1:

_{2}*S*×_{1}*D*,_{2}*S*×_{3}*D*(_{4}*S*rotated 22.5 degrees and_{1}*D*rotated 45 degrees),_{2}*S*×_{5}*D*(_{6}*S*rotated 45 degrees and_{1}*D*rotated 90 degrees),_{2}*S*×_{7}*D*(_{8}*S*rotated 67.5 degrees and_{1}*D*rotated 135 degrees)._{2}

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