# Great transitional 13-5 double step prism

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

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

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 52 irregular tetrahedra, 52 phyllic disphenoids, 13 tetragonal disphenoids, 26 bilaterally-symmetric notches |

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

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

Vertices | 26 |

Vertex figure | 15-vertex polyhedron with 3 tetragons and 20 triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Great 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 **great transitional 13-5 double step prism** is a convex isogonal polychoron that consists of 26 bilaterally-symmetric notches, 13 tetragonal disphenoids, 52 phyllic disphenoids, and 52 irregular tetrahedra. 5 bilaterally-symmetric notches, 2 tetragonal disphenoids, 8 phyllic disphenoids, and 8 irregular tetrahedra 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 approximately 1:2.98928.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a great 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* ≈ 0.1342686996111878133300549, *b* ≈ 2.0223594019664291689707605 and *k* is an integer from 0 to 12.