# Great enneagrammic prism

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Great enneagrammic prism | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Gistep |

Info | |

Coxeter diagram | x x9/4o |

Symmetry | I2(9)×A1, order 36 |

Army | Semi-uniform Ep |

Regiment | Gistep |

Elements | |

Vertex figure | Isosceles triangle, edge lengths √2, √2, 2cos(4π/9) |

Faces | 9 squares, 2 great enneagrams |

Edges | 9+18 |

Vertices | 18 |

Measures (edge length 1) | |

Circumradius | √1+1/sin^{2}(4π/9)/2 ≈ 0.71258 |

Volume | 9/(4tan(4π/9)) ≈ 0.39674 |

Dihedral angles | 4–9/4: 90° |

4–4: 20° | |

Height | 1 |

Central density | 4 |

Euler characteristic | 2 |

Related polytopes | |

Dual | Great enneagrammic bipyramid |

Conjugates | Enneagonal prism, Enneagrammic prism |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **great enneagrammic prism**, or **gistep**, is a prismatic uniform polyhedron. It consists of 2 great enneagrams and 9 squares. Each vertex joins one great enneagram and two squares. As the name suggests, it is a prism based on a great enneagram.

## Vertex coordinates[edit | edit source]

The coordinates of a great enneagrammic prism, centered at the origin and with edge length 2sin(4π/9), are given by:

- (1, 0, ±sin(4π/9)),
- (cos(2π/9), ±sin(2π/9), ±sin(4π/9)),
- (cos(4π/9), ±sin(4π/9), ±sin(4π/9)),
- (–1/2, ±√3/2), ±sin(4π/9)),
- (cos(8π/9), ±sin(8π/9), ±sin(4π/9)).

## External links[edit | edit source]

- Wikipedia Contributors. "Enneagrammic prism".