# 35-6 step prism

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35-6 step prism | |
---|---|

File:35-6 step prism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 70+70+70+70 phyllic disphenoids |

Faces | 140+140+140 scalene triangles, 70+70 isosceles triangles |

Edges | 35+70+70+70+70 |

Vertices | 35 |

Vertex figure | 18-vertex polyhedron with 32 triangular faces |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | 35-6 gyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(35)-6)×2R, order 140 |

Convex | Yes |

Nature | Tame |

The **35-6 step prism** is a convex isogonal polychoron, member of the step prism family. It has 280 phyllic disphenoids of four kinds as cells. 32 disphenoids join at each vertex. It is also the 35-29 step prism.

The ratio between the longest and shortest edges is 1: ≈ 1:1.98552.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 35-6 step prism of circumradius √2 are given by:

- (sin(2π
*k*/35), cos(2π*k*/35), sin(12π*k*/35), cos(12π*k*/35)),

where *k* is an integer from 0 to 34.