# 19-3 step prism

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19-3 step prism | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Info | |

Symmetry | I2(19)+×2×I, order 38 |

Elements | |

Vertex figure | 14-vertex polyhedron with 24 triangular faces |

Cells | 19+19+19+19+19+19 phyllic disphenoids |

Faces | 19+19+38+38+38+38+38 scalene triangles |

Edges | 19+19+19+19+19+19+19 |

Vertices | 19 |

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

Edge lengths | 12-valence (19): |

6-valence (19): | |

3-valence (19): | |

4-valence (19): | |

4-valence (19): | |

4-valence (19): | |

4-valence (19): | |

Central density | 1 |

Euler characteristic | 0 |

Related polytopes | |

Dual | 19-3 gyrochoron |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **19-3 step prism** is a convex isogonal polychoron and a member of the step prism family. It has 114 phyllic disphenoids of six kinds as cells, with 24 joining at each vertex. It can also be constructed as the 19-6 step prism.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 19-3 step prism inscribed in an enneadecagonal duoprism with base lengths *a* and *b* are given by:

- (
*a**sin(2π*k*/19),*a**cos(2π*k*/19),*b**sin(6π*k*/19),*b**cos(6π*k*/19)),

where *k* is an integer from 0 to 18.
If the edge length differences are to be minimized, the ratio of *a:b* must be equivalent to 1: ≈ 1:1.83802.

## External links[edit | edit source]

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