# 40-9 step prism

The **40-9 step prism**, also known as the **digonal double pentaswirlprism**, is a convex isogonal polychoron, member of the step prism family. It has 40 rhombic disphenoids and 240 phyllic disphenoids of three kinds as cells. 4 rhombic and 24 phyllic disphenoids join at each vertex. It is the fourth in an infinite family of isogonal digonal prismatic swirlchora.

40-9 step prism | |
---|---|

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 80+80+80 phyllic disphenoids, 40 rhombic disphenoids |

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

Edges | 40+40+80+80+80 |

Vertices | 40 |

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

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | 40-9 gyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(40)-9)×2R, order 160 |

Convex | Yes |

Nature | Tame |

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

## Vertex coordinates edit

Coordinates for the vertices of a 40-9 step prism of circumradius √2 are given by:

- (sin(π
*k*/20), cos(π*k*/20), sin(9π*k*/20), cos(9π*k*/20)),

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