# Great ditrigonary icosidodecahedral antiprism

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Great ditrigonary icosidodecahedral antiprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gidtidap |

Coxeter diagram | |

Elements | |

Cells | 40 tetrahedra, 12 pentagonal antiprisms, 2 great ditrigonary icosidodecahedra |

Faces | 40+120 triangles, 24 pentagons |

Edges | 60+120 |

Vertices | 40 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | 0 |

Dichoral angles | Gidtid–3–tet: |

Tet–3–pap: | |

Gidtid–5–pap: | |

Height | |

Related polytopes | |

Army | Semi-uniform Dope |

Regiment | Sidtidap |

Dual | Great triambic icosahedral antitegum |

Abstract & topological properties | |

Euler characteristic | –10 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | No |

Nature | Tame |

The **great ditrigonary icosidodecahedral antiprism** or **gidtidap**, is a nonconvex uniform polychoron that consists of 2 great ditrigonary icosidodecahedra, 12 pentagonal antiprisms, and 40 tetrahedra. Each vertex joins 1 great ditrigonary icosidodecahedron, 3 pentagonal antiprisms, and 4 tetrahedra.

The pentagonal antiprism cells pass through the center of the polychoron, making it a hemipolychoron.

## 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" (#968).

- Klitzing, Richard. "gidtidap".