# Enneagrammic prism

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Enneagrammic prism | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Step |

Coxeter diagram | x x9/2o () |

Elements | |

Faces | 9 squares, 2 enneagrams |

Edges | 9+18 |

Vertices | 18 |

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–4: 100° |

4–9/2: 90° | |

Height | 1 |

Central density | 2 |

Number of external pieces | 20 |

Level of complexity | 6 |

Related polytopes | |

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

Regiment | Step |

Dual | Enneagrammic tegum |

Conjugates | Enneagonal prism, Great enneagrammic prism |

Convex core | Enneagonal prism |

Abstract & topological properties | |

Flag count | 108 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | I_{2}(9)×A_{1}, order 36 |

Convex | No |

Nature | Tame |

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

## Vertex coordinates[edit | edit source]

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

- (1, 0, \pmsin(2π/9)),
- (cos(2π/9), \pmsin(2π/9), \pmsin(2π/9)),
- (cos(4π/9), \pmsin(4π/9), \pmsin(2π/9)),
- (–1/2, \pm√3/2, \pmsin(2π/9)),
- (cos(8π/9), \pmsin(8π/9), \pmsin(2π/9)).

## External links[edit | edit source]

- Wikipedia contributors. "Enneagrammic prism".