# Transitional 12-5 double gyrostep prism

Jump to navigation
Jump to search

Transitional 12-5 double gyrostep prism | |
---|---|

File:Transitional 12-5 double gyrostep prism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 24 phyllic disphenoids, 24 tetragonal disphenoids, 24 tetragonal antiwedges |

Faces | 48 scalene triangles, 48+48 isosceles triangles, 24 kites |

Edges | 24+24+24+48 |

Vertices | 24 |

Vertex figure | Polyhedron with 2 tetragons and 12 triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Transitional 12-5 antibigyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(12)-5)×2I, order 48 |

Convex | Yes |

Nature | Tame |

The **transitional 12-5 double gyrostep prism** is a convex isogonal polychoron that consists of 24 tetragonal antiwedges, 24 tetragonal disphenoids, and 24 phyllic disphenoids. 6 tetragonal antiwedges, 4 tetragonal disphenoids, and 4 phyllic disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal 12-5 step prisms.

The ratio between the longest and shortest edges is 1: ≈ 1:2.61313.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a transitional 12-5 double gyrostep prism are given by:

- (
*a**sin(2π*k*/12),*a**cos(2π*k*/12),*b**sin(10π*k*/12),*b**cos(10π*k*/12)), - (
*b**sin(2π*k*/12),*b**cos(2π*k*/12),*a**sin(10π*k*/12),*a**cos(10π*k*/12)),

where *a* = √36-6√18-12√2/12, *b* = √36+6√18-12√2/12 and *k* is an integer from 0 to 11.

## External links[edit | edit source]

- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".