# Small transitional 30-11 double gyrostep prism

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Small transitional 30-11 double gyrostep prism | |
---|---|

File:Small transitional 30-11 double gyrostep prism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 60 tetrahedra, 60 skew rectangular tegums |

Faces | 60+120 isosceles triangles, 60+120 triangles |

Edges | 60+60+60+120 |

Vertices | 60 |

Vertex figure | Polyhedron with 4 tetragons and 6 triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Small transitional 30-11 antibigyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(30)-11)×2I, order 120 |

Convex | Yes |

Nature | Tame |

The **small transitional 30-11 double gyrostep prism** is a convex isogonal polychoron that consists of 60 skew rectangular tegums and 60 tetrahedra. 6 skew rectangular tegums and 4 tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 30-11 step prisms.

It can also be obtained as a diminishing of the hexacosichoron and is also a vertex-faceting of the grand antiprism.

The ratio between the longest and shortest edges is 1: ≈ 1:1.61803.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a small transitional 30-11 double gyrostep prism are given by:

- (
*a**sin(π*k*/15),*a**cos(π*k*/15),*b**sin(11π*k*/15),*b**cos(11π*k*/15)), - (
*b**sin(π*k*/15),*b**cos(π*k*/15), -*a**sin(11π*k*/15), -*a**cos(11π*k*/15)),

where and *k* is an integer from 0 to 29.