# Grand hendecagrammic prism

The **grand hendecagrammic prism** or **gashenp** is a prismatic uniform polyhedron. It consists of 2 grand hendecagrams and 11 squares. Each vertex joins one grand hendecagram and two squares. As the name suggests, it is a prism based on a grand hendecagram.

Grand hendecagrammic prism | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Gashenp |

Coxeter diagram | x x11/5o () |

Elements | |

Faces | 11 squares, 2 grand hendecagrams |

Edges | 11+22 |

Vertices | 22 |

Vertex figure | Isosceles triangle, edge lengths √2, √2, 2cos(5π/11) |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–11/5: 90° |

4–4: | |

Height | 1 |

Central density | 5 |

Number of external pieces | 24 |

Level of complexity | 6 |

Related polytopes | |

Army | Semi-uniform Henp, edge lengths (base), 1 (sides) |

Regiment | Gashenp |

Dual | Grand hendecagrammic tegum |

Conjugates | Hendecagonal prism, Small hendecagrammic prism, Hendecagrammic prism, Great hendecagrammic prism |

Convex core | Hendecagonal prism |

Abstract & topological properties | |

Flag count | 132 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | I_{2}(11)×A_{1}, order 44 |

Convex | No |

Nature | Tame |

## Vertex coordinates edit

The coordinates of a grand hendecagrammic prism, centered at the origin and with edge length 2sin(5π/11), are given by:

- (1, 0, \pmsin(5π/11)),
- (cos(2π/11), \pmsin(2π/11), \pmsin(5π/11)),
- (cos(4π/11), \pmsin(4π/11), \pmsin(5π/11)),
- (cos(6π/11), \pmsin(6π/11), \pmsin(5π/11)),
- (cos(8π/11), \pmsin(8π/11), \pmsin(5π/11)),
- (cos(10π/11), \pmsin(10π/11), \pmsin(5π/11)).