# 41-9 step prism

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41-9 step prism | |
---|---|

File:41-9 step prism.png | |

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 82+82+82 phyllic disphenoids, 41 tetragonal disphenoids |

Faces | 164+164 scalene triangles, 82+164 isosceles triangles |

Edges | 82+82+82+82 |

Vertices | 41 |

Vertex figure | 16-vertex polyhedron with 28 triangular faces |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | 41-9 gyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(37)-6)×2I, order 164 |

Convex | Yes |

Nature | Tame |

The **41-9 step prism** is a convex isogonal polychoron, member of the step prism family. It has 41 tetragonal disphenoids and 246 phyllic disphenoids of three kinds as cells. 4 tetragonal and 24 phyllic disphenoids join at each vertex. It is also the 41-32 step prism.

The ratio between the longest and shortest edges is 1: ≈ 1:2.06812.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 41-9 step prism of circumradius √2 are given by:

- (sin(2π
*k*/41), cos(2π*k*/41), sin(18π*k*/41), cos(18π*k*/41)),

where *k* is an integer from 0 to 40.