# 34-13 step prism

The **34-13 step prism** is a convex isogonal polychoron, member of the step prism family. It has 34 tetragonal disphenoids and 136 phyllic disphenoids of two kinds as cells. 4 tetragonal and 16 phyllic disphenoids join at each vertex. It is also the 34-21 step prism.

34-13 step prism | |
---|---|

File:34-13 step prism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 68+68 phyllic disphenoids, 34 tetragonal disphenoids |

Faces | 136 scalene triangles, 68+136 isosceles triangles |

Edges | 68+68+68 |

Vertices | 30 |

Vertex figure | 12-vertex polyhedron with 20 triangular faces |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | 34-13 gyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(34)-13)×2I, order 136 |

Convex | Yes |

Nature | Tame |

The ratio between the longest and shortest edges is 1: ≈ 1:1.79149.

## Vertex coordinatesEdit

Coordinates for the vertices of a 34-13 step prism of circumradius √2 are given by:

- (sin(π
*k*/17), cos(π*k*/17), sin(13π*k*/17), cos(13π*k*/17)),

where *k* is an integer from 0 to 33.