# Medial 13-5 double step prism

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

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

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

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

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

Vertices | 26 |

Vertex figure | 13-vertex polyhedron with 22 triangular faces |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Medial 13-5 bigyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I2(13)+×4×I, order 52 |

Convex | Yes |

Nature | Tame |

The **medial 13-5 double step prism** is a convex isogonal polychoron that consists of 13 tetragonal disphenoids, 26 phyllic disphenoids, and 104 irregular tetrahedra of two kinds. 2 tetragonal disphenoids, 4 phyllic disphenoids, and 16 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 13-5 step prisms.

This polychoron cannot be optimized using the ratio method, because the solution (*a*/*b* = (2+√4+2cos(π/13)+2sin(3π/26))/(2cos(2π/13)) would yield a small 13-5 double step prism instead.