# Small 15-4 double step prism

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Small 15-4 double step prism | |
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File:Small 15-4 double step prism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 15 rhombic disphenoids, 30+30+30 phyllic disphenoids, 60 irregular tetrahedra |

Faces | 30 isosceles triangles, 60+60+60+60+60 scalene triangles |

Edges | 15+30+30+30+30+60 |

Vertices | 30 |

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

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Small 15-4 bigyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I2(15)+×4×I, order 60 |

Convex | Yes |

Nature | Tame |

The **small 15-4 double step prism** is a convex isogonal polychoron that consists of 15 rhombic disphenoids, 90 phyllic disphenoids of three kinds, and 60 irregular tetrahedra. 2 rhombic disphenoids, 12 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 15-4 step prisms.

This polychoron cannot be optimized using the ratio method, because the solution would yield a medial 15-4 double step prism instead.