# 13-5 step prism

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13-5 step prism | |
---|---|

File:13-5 step prism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 26 phyllic disphenoids, 13 tetragonal disphenoids |

Faces | 26+52 isosceles triangles |

Edges | 26+26 |

Vertices | 13 |

Vertex figure | Prodigonal antiprismatic symmetric snub disphenoid |

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

Edge lengths | 5-valence (26): |

4-valence (26): | |

Central density | 1 |

Related polytopes | |

Dual | 13-5 gyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(13)-5)×2I, order 52 |

Convex | Yes |

Nature | Tame |

The **13-5 step prism** is a convex isogonal polychoron and a member of the step prism family. It has 13 tetragonal disphenoids and 26 phyllic disphenoids as cells. 4 tetragonal and 8 phyllic disphenoids join at each vertex. It is also the pentagonal funk tegum.

Compared to other 13-vertex step prisms, this polychoron has doubled symmetry, because 13 is a factor of 5^{2}+1 = 26.

Its vertex figure is topologically equivalent to the Johnson solid snub disphenoid.

The ratio between the longest and shortest edges is 1: ≈ 1:1.19192.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 13-5 step prism of circumradius √2 are given by:

- (sin(2π
*k*/13), cos(2π*k*/13), sin(10π*k*/13), cos(10π*k*/13)),

where *k* is an integer from 0 to 12.

## Isogonal derivatives[edit | edit source]

Substitution by vertices of these following elements will produce these convex isogonal polychora:

- Tetragonal disphenoid (13): 13-5 step prism
- Edge (26): Small 13-5 double step prism
- Edge (26): Small 13-5 double gyrostep prism

## External links[edit | edit source]

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