# 15-4 step prism

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15-4 step prism | |
---|---|

File:15-4 step prism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 30+30 phyllic disphenoids |

Faces | 60 scalene triangles, 30+30 isosceles triangles |

Edges | 15+30+30 |

Vertices | 15 |

Vertex figure | Paratetraaugmented digonal scalenohedron |

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

Edge lengths | 6-valence (30): |

6-valence (15): | |

3-valence (30): | |

Central density | 1 |

Related polytopes | |

Dual | 15-4 gyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(15)-4)×2R, order 60 |

Convex | Yes |

Nature | Tame |

The **15-4 step prism** is a convex isogonal polychoron and a member of the step prism family. It has 60 phyllic disphenoids of two kinds as cells, with 16 joining at each vertex.

Compared to other 15-vertex step prisms, this polychoron has doubled symmetry, because 15 is a factor of 4^{2}-1 = 15.

The ratio between the longest and shortest edges is 1: ≈ 1:1.39239.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 15-4 step prism of circumradius √2 are given by:

- (sin(2π
*k*/15), cos(2π*k*/15), sin(8π*k*/15), cos(8π*k*/15)),

where *k* is an integer from 0 to 14.

## External links[edit | edit source]

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