# Great duoantiprism

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 |

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.

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 links[edit | edit source]

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

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

- Klitzing, Richard. "Gudap".