# 16-6 step prism

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16-6 step prism | |
---|---|

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 16+16+16 phyllic disphenoids, 8 rhombic disphenoids |

Faces | 32+32+32 scalene triangles, 16 isosceles triangles |

Edges | 8+16+16+16+16 |

Vertices | 16 |

Vertex figure | Edge-expanded hexagonal tegum |

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

Edge lengths | 6-valence (16): |

5-valence (16): | |

4-valence (16): | |

4-valence (16): | |

4-valence (8): 2 | |

Central density | 1 |

Related polytopes | |

Dual | 16-6 gyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(16)-6), order 32 |

Convex | Yes |

Nature | Tame |

The **16-6 step prism** is a convex isogonal polychoron and a member of the step prism family. It has 8 rhombic disphenoids and 48 phyllic disphenoids of three kinds as cells, with 14 (2 rhombic and 12 phyllic disphenoids) joining at each vertex. It is also the hexagonal funk tegum.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.45294.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 16-6 step prism inscribed in a hexadecagonal duoprism with base lengths *a* and *b* are given by:

- ,

where *k* is an integer from 0 to 15.
If the edge length differences are to be minimized, the ratio of *a:b* must be equivalent to 1: ≈ 1:1.06159.

## External links[edit | edit source]

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