# 17-4 step prism

Jump to navigation
Jump to search

17-4 step prism | |
---|---|

File:17-4 step prism.png | |

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 34+34 phyllic disphenoids, 17 tetragonal disphenoids |

Faces | 68 scalene triangles, 34+68 isosceles triangles |

Edges | 34+34+34 |

Vertices | 17 |

Vertex figure | Paratetraaugmented triakis tetragonal disphenoid |

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

Edge lengths | 8-valence (34): |

4-valence (34): | |

3-valence (34): | |

Central density | 1 |

Related polytopes | |

Dual | 17-4 gyrochoron |

Abstract & topological properties | |

Flag count | 2040 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(17)-4)×2I, order 68 |

Convex | Yes |

Nature | Tame |

The **17-4 step prism** is a convex isogonal polychoron, member of the step prism family. It has 17 tetragonal disphenoids and 68 phyllic disphenoids of two kinds as cells. 2 tetragonal and 16 phyllic disphenoids join at each vertex.

Compared to other 17-vertex step prisms, this polychoron has doubled symmetry, because 17 is a factor of 4^{2}+1 = 17.

The ratio between the longest and shortest edges is 1: ≈ 1:1.51687.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 17-4 step prism of circumradius √2 are given by:

- ,

where *k* is an integer from 0 to 16.

## External links[edit | edit source]

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