# 40-9 step prism

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

Rank | 4 |

Type | Isogonal |

Space | Spherical |

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 **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.

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

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 40-9 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.