# Great duoantiprism

The **great duoantiprism** or **gudap**, also known as the **pentagonal-pentagrammic crossed duoantiprism** or **5-5/3 duoantiprism**, is a nonconvex uniform polychoron that consists of 50 tetrahedra, 10 pentagonal antiprisms, and 10 pentagrammic retroprisms. 4 tetrahedra, 2 pentagonal antiprisms, and 2 pentagrammic retroprisms join at each vertex.

Great duoantiprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Gudap |

Info | |

Coxeter diagram | s10o2s10/3o |

Symmetry | I2(10)×I2(10)/2, order 200 |

Army | Pentagonal-pentagonal duoantiprism |

Regiment | Gudap |

Elements | |

Vertex figure | Semicrossed gyrobifastigium, edge lengths (√5-1)/2, 1 and (√5+1)/2 |

Cells | 50 tetrahedra, 10 pentagonal antiprisms, 10 pentagrammic retroprisms |

Faces | 100+100 triangles, 10 pentagons, 10 pentagrams |

Edges | 50+50+100 |

Vertices | 50 |

Measures (edge length 1) | |

Circumradius | 1 |

Hypervolume | |

Dichoral angles | Starp–5/2–starp: 144° |

Starp–3–tet: | |

Pap–5–pap: 72° | |

Pap–3–tet: | |

Central density | 3 |

Euler characteristic | 0 |

Number of pieces | 600 |

Level of complexity | 144 |

Related polytopes | |

Dual | Pentagonal-pentagrammic concave duoantitegum |

Conjugate | Great duoantiprism |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

It is one of only two members of the infinite set of duoantiprisms that can be made uniform, the other being the hexadecachoron. It can be obtained through the process of alternating a non-uniform decagonal-decagrammic duoprism where the decagrams have an edge length of times that of its decagons.

The great duoantiprism can be vertex-inscribed into a small stellated hecatonicosachoron. In fact it occurs as a subsymmetrical faceting of that polychoron, with the pentagrammic retroprisms being facetings of a ring of 10 small stellated dodecahedral cells.

## External linksEdit

- Bowers, Jonathan. "Category 20: Miscellaneous" (#965).

- Bowers, Jonathan. "How to Make Gudap".

- Klitzing, Richard. "Gudap".