# Small transitional 13-5 double step prism

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Small transitional 13-5 double step prism | |
---|---|

File:Small transitional 13-5 double step prism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 13 tetragonal disphenoids, 26 bilaterally-symmetric octahedra |

Faces | 52 scalene triangles, 26+52 isosceles triangles |

Edges | 13+26+26+52 |

Vertices | 26 |

Vertex figure | 9-vertex polyhedron with 6 tetragons and 2 triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Small transitional 13-5 bigyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

The **small transitional 13-5 double step prism** is a convex isogonal polychoron that consists of 26 bilaterally-symmetric octahedra and 13 tetragonal disphenoids. 6 bilaterally-symmetric octahedra and 2 tetragonal disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal 13-5 step prisms.

The ratio between the longest and shortest edges is 1:*a* ≈ 1:2.15664, where *a* is the largest real root of a^{6}-7a^{4}+12a^{2}-5.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a small transitional 13-5 double step prism are given by:

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

where *a* = 1/(√2(sin(5π/26)csc(π/26)-1)), *b* = sin(5π/26)/(√2(sin(5π/26)-sin(π/26))) and *k* is an integer from 0 to 12.