# Square-square prismantiprismoid

Square-square prismantiprismoid | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Sispap |

Coxeter diagram | x4s2s8o () |

Elements | |

Cells | 16 wedges, 8 rectangular trapezoprisms, 4 square prisms, 4 square antiprisms |

Faces | 32 isosceles triangles, 32 isosceles trapezoids, 8+16 rectangles, 8 squares |

Edges | 16+16+32+32 |

Vertices | 32 |

Vertex figure | Monoaugmented isosceles trapezoidal pyramid |

Measures (as derived from unit-edge octagonal duoprism) | |

Edge lengths | Short edges of rectangles (16): 1 |

Side edges (32): | |

Edges of squares (32): | |

Long edges of rectangles (16): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Sispap |

Regiment | Sispap |

Dual | Square-square tegmantitegmoid |

Abstract & topological properties | |

Flag count | 1408 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | (B_{2}×I_{2}(8))/2, order 64 |

Convex | Yes |

Nature | Tame |

The **square-square prismantiprismoid** or **sispap**, also known as the **edge-snub square-square duoprism** or **4-4 prismantiprismoid**, is a convex isogonal polychoron that consists of 4 square antiprisms, 4 square prisms, 8 rectangular trapezoprisms, and 16 wedges. 1 square prism, 1 square antiprism, 2 rectangular trapezoprisms, and 3 wedges join at each vertex. It can be obtained through the process of alternating one class of edges of the octagonal duoprism so that one ring of octagons become rectangles. However, it cannot be made uniform, as it generally has 4 edge lengths, which can be minimized to no fewer than 2 different sizes.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.64463.

## Vertex coordinates[edit | edit source]

The vertices of a square-square prismantiprismoid based on an octagonal duoprism of edge length 1, centered at the origin, are given by: