# 40-11 step prism

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40-11 step prism | |
---|---|

File:40-11 step prism.png | |

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 80+80+80 phyllic disphenoids |

Faces | 160+160 scalene triangles, 80+80 isosceles triangles |

Edges | 40+80+80+80 |

Vertices | 40 |

Vertex figure | 14-vertex polyhedron with 24 triangular faces |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | 40-11 gyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(40)-11)×2R, order 160 |

Convex | Yes |

Nature | Tame |

The **40-11 step prism** is a convex isogonal polychoron, member of the step prism family. It has 240 phyllic disphenoids of three kinds as cells. 24 disphenoids join at each vertex.

The ratio between the longest and shortest edges is 1: ≈ 1:2.28825.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 40-11 step prism of circumradius √2 are given by:

- (sin(π
*k*/20), cos(π*k*/20), sin(11π*k*/20), cos(11π*k*/20)),

where *k* is an integer from 0 to 39.