# Great duoantiprism

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

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gudap |

Coxeter diagram | s10o2s10/3o () |

Elements | |

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

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

Edges | 50+50+100 |

Vertices | 50 |

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

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 |

Number of external pieces | 600 |

Level of complexity | 144 |

Related polytopes | |

Army | Pentagonal-pentagonal duoantiprism |

Regiment | Gudap |

Dual | Pentagonal-pentagrammic concave duoantitegum |

Conjugate | Great duoantiprism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | (I_{2}(10)×I_{2}(10))/2, order 200 |

Convex | No |

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 contains the vertices of an inscribed pentagonal-pentagrammic duoprism, and in turn can be vertex-inscribed into a small stellated hecatonicosachoron. In fact, it can be derived as a subsymmetric faceting of that polychoron, with the pentagrammic retroprisms being facetings of a ring of 10 small stellated dodecahedral cells and the pentagonal antiprisms being facetings of a ring of 10 great dodecahedral cells.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The coordinates of a great duoantiprism, centered at the origin and with unit edge length, are given by:

## External links[edit | edit source]

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

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

- Klitzing, Richard. "gudap".

- Wikipedia Contributors. "Great duoantiprism".