# Digonal-square duoantiprism

Digonal-square duoantiprism | |
---|---|

File:Digonal-square duoantiprism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Notation | |

Bowers style acronym | Disdap |

Coxeter diagram | s4o2s8o () |

Elements | |

Cells | 16 digonal disphenoids, 8 tetragonal disphenoids, 4 square antiprisms |

Faces | 32+32 isosceles triangles, 4 squares |

Edges | 8+16+32 |

Vertices | 16 |

Vertex figure | Augmented triangular prism |

Measures (based on polygons of edge length 1) | |

Edge lengths | Lacing (32): |

Digons (8): 1 | |

Edges of squares (16): 1 | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Disdap |

Regiment | Disdap |

Dual | Digonal-square duoantitegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

The **digonal-square duoantiprism** or **disdap**, also known as the **2-4 duoantiprism** or the **8-2 double step prism**, is a convex isogonal polychoron that consists of 4 square antiprisms, 8 tetragonal disphenoids, and 16 digonal disphenoids. 2 square antiprisms, 2 tetragonal disphenoids, and 4 digonal disphenoids join at each vertex. It can be obtained through the process of alternating the square-octagonal duoprism. However, it cannot be made uniform, as it generally has 3 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: ≈ 1:1.12303.

## Vertex coordinates[edit | edit source]

The vertices of a digonal–square duoantiprism, assuming that the square antiprisms are uniform of edge length 1, centered at the origin, are given by:

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by: