# Digonal double antiprismoid

Digonal double antiprismoid | |
---|---|

File:Digonal double antiprismoid.png | |

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Didiap |

Elements | |

Cells | 32 sphenoids, 8+16 tetragonal disphenoids |

Faces | 16+32+64 isosceles triangles |

Edges | 8+32+32 |

Vertices | 16 |

Vertex figure | Hexakis digonal-hexagonal gyrowedge |

Measures (for variant with minimal differences in edge lengths) | |

Edge lengths | Base edges of antiprismatic disphenoids (8): 1 |

Lacing edges of side disphenoids (32): 1 | |

Side edges of antiprismatic disphenoids (32): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Didiap |

Regiment | Didiap |

Dual | Digonal double antitegmoid |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}+≀S_{2}×2, order 64 |

Convex | Yes |

Nature | Tame |

The **digonal double antiprismoid** or **didiap** is a convex isogonal polychoron and the first member of the double antiprismoid family. It consists of 24 tetragonal disphenoids of two kinds and 32 sphenoids. 6 disphenoids and 8 sphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal digonal-digonal duoantiprisms or by alternating the square ditetragoltriate. However, it cannot be made uniform. As such it is one of a number of polychora that can be obtained as the convex hull of two variant hexadecachora. It is the first in an infinite family of isogonal digonal antiprismatic swirlchora.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.34500. This variant is formed from duoantiprisms with base digons of length ratio 1: ≈ 1:1.61803.

## Vertex coordinates[edit | edit source]

The vertices of a digonal double antiprismoid, assuming that the two short edges have edge length 1, centered at the origin, are given by: