# 17-2 step prism

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17-2 step prism | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 17+17+17+17+17+17+17 phyllic disphenoids |

Faces | 34+34+34+34+34+34 scalene triangles, 17+17 isosceles triangles |

Edges | 17+17+17+17+17+17+17+17 |

Vertices | 17 |

Vertex figure | Ridge-quintitriakis bi-apiculated tetrahedron |

Measures (circumradius , based on a uniform duoprism) | |

Edge lengths | 15-valence (17): |

3-valence (17): | |

4-valence (17): | |

4-valence (17): | |

4-valence (17): | |

4-valence (17): | |

4-valence (17): | |

4-valence (17): | |

Central density | 1 |

Related polytopes | |

Dual | 17-2 gyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(17)-2), order 34 |

Convex | Yes |

Nature | Tame |

The **17-2 step prism** is a convex isogonal polychoron and a member of the step prism family. It has 119 phyllic disphenoids of seven kinds as cells, with 28 joining at each vertex. It can also be constructed as the 17-8 step prism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.78329.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 17-2 step prism inscribed in a heptadecagonal duoprism with base lengths *a* and *b* are given by:

- (
*a**sin(2π*k*/17),*a**cos(2π*k*/17),*b**sin(4π*k*/17),*b**cos(4π*k*/17)),

where *k* is an integer from 0 to 16.
If the edge length differences are to be minimized, the ratio of *a:b* must be equivalent to 1: ≈ 1:3.14656.

## External links[edit | edit source]

- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".