# Small 13-5 double step prism

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

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

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 52 irregular tetrahedra, 26+26 phyllic disphenoids, 13 tetragonal disphenoids |

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

Edges | 13+26+26+26+52 |

Vertices | 26 |

Vertex figure | Bilaterally-symmetric octakis digonal-octagonal gyrowedge |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Small 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 13-5 double step prism** is a convex isogonal polychoron that consists of 13 tetragonal disphenoids, 52 phyllic disphenoids of two kinds and 52 irregular tetrahedra obtained as the convex hull of two orthogonal 13-5 step prisms.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is approximately 1:1.58440.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a small 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* = √2/(2sec(2π/13)+sec(2π/13)√4+2cos(π/13)+2sin(3π/26)-2), *b* = (√2+√2+cos(π/13)+sin(3π/26))/(2-2cos(2π/13)+√4+2cos(π/13)+2sin(3π/26)) and *k* is an integer from 0 to 12.

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