# 18-5 step prism

The **18-5 step prism**, also known as the **9-2 double step prism**, is a convex isogonal polychoron and a member of the step prism family. It has 72 phyllic disphenoids of four kinds as cells, with 16 joining at each vertex. It can also be constructed as the 18-7 step prism, or as the convex hull of two opposite 9-2 step prisms.

18-5 step prism | |
---|---|

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 18+18+18+18 phyllic disphenoids |

Faces | 36+36+36 scalene triangles, 18+18 isosceles triangles |

Edges | 18+18+18+18+18 |

Vertices | 18 |

Vertex figure | Metabitriakis snub disphenoid |

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

Edge lengths | 6-valence (18): |

5-valence (18): | |

6-valence (18): | |

4-valence (18): | |

3-valence (18): | |

Central density | 1 |

Related polytopes | |

Dual | 18-5 gyrochoron |

Abstract & topological properties | |

Flag count | 1728 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(18)-5), order 36 |

Convex | Yes |

Nature | Tame |

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.41421.

## Vertex coordinates Edit

Coordinates for the vertices of an 18-5 step prism inscribed in an octadecagonal duoprism with base lengths *a* and *b* are given by:

- ,

where *k* is an integer from 0 to 17.
If the edge length differences are to be minimized, the ratio of *a:b* must be equivalent to 1: ≈ 1:0.90289.

## External links Edit

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