# Ditrigonary dodecadodecahedral antiprism

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Ditrigonary dodecadodecahedral antiprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Ditdidap |

Elements | |

Cells | 12 pentagonal antiprisms, 12 pentagrammic antiprisms, 2 ditrigonary dodecadodecahedra |

Faces | 120 triangles, 24 pentagons, 24 pentagrams |

Edges | 60+120 |

Vertices | 40 |

Vertex figure | Inverted retrotriangular cupola, edge lengths (√5–1)/2, (1+√5)/2 (3 base edges), 1 (remaining edges) |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Ditdid–5–pap: |

Ditdid–5/2–stap: 90° | |

Stap–3–pap: | |

Height | |

Number of external pieces | 518 |

Level of complexity | 78 |

Related polytopes | |

Army | Semi-uniform Dope |

Regiment | Sidtidap |

Dual | Medial triambic icosahedral antitegum |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | No |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | No |

Nature | Tame |

The **ditrigonary dodecadodecahedral antiprism** is a nonconvex uniform polychoron that consists of 2 ditrigonary dodecadodecahedra, 12 pentagonal antiprisms, and 12 pentagrammic antiprisms. Each vertex joins 1 ditrigonary dodecadodecahedron, 3 pentagrammic antiprisms, and 3 pentagonal antiprisms.

The pentagonal antiprism cells pass through the center of the polychoron.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small ditrigonary icosidodecahedral antiprism.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 20: Miscellaneous" (#967).

- Klitzing, Richard. "ditdidap".