# 14-2 step prism

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14-2 step prism | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 14+14+14+14+14 phyllic disphenoids, 7 rhombic disphenoids |

Faces | 28+28+28+28+28 scalene triangles, 14 isosceles triangles |

Edges | 7+14+14+14+14+14+14 |

Vertices | 14 |

Vertex figure | Ridge-quadritriakis notch |

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

Edge lengths | 12-valence (14): |

3-valence (14): | |

4-valence (7): 2 | |

4-valence (14): | |

4-valence (14): | |

4-valence (14): | |

4-valence (14): | |

Central density | 1 |

Related polytopes | |

Dual | 14-2 gyrochoron |

Abstract properties | |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(14)-2), order 28 |

Convex | Yes |

Nature | Tame |

The **14-2 step prism** is a convex isogonal polychoron and a member of the step prism family. It has 7 rhombic disphenoids and 70 phyllic disphenoids of five kinds as cells, with 22 (2 rhombic and 20 phyllic disphenoids) joining at each vertex.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.35298.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 14-2 step prism inscribed in a tetradecagonal duoprism with base lengths *a* and *b* are given by:

- (
*a**sin(π*k*/7),*a**cos(π*k*/7),*b**sin(2π*k*/7),*b**cos(2π*k*/7)),

where *k* is an integer from 0 to 13.
If the edge length differences are to be minimized, the ratio of *a:b* must be equivalent to 1: ≈ 1:2.24698.

## External links[edit | edit source]

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