# Small transitional 12-5 double step prism

Jump to navigation
Jump to search

Small transitional 12-5 double step prism | |
---|---|

File:Small transitional 12-5 double step prism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 12 tetragonal disphenoids, 12 rectangular gyroprisms |

Faces | 24+48 isosceles triangles, 12 rectangles |

Edges | 12+24+24+24 |

Vertices | 24 |

Vertex figure | Digonal-rectangular gyronotch |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Small transitional 12-5 bigyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

The **small transitional 12-5 double step prism** is a convex isogonal polychoron that consists of 12 rectangular gyroprisms and 12 tetragonal disphenoids. 2 rectangular gyroprisms and 4 tetragonal 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: ≈ 1:1.73205.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a small transitional 12-5 double step 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* = (√3-1)/4, *b* = (1+√3)/4 and *k* is an integer from 0 to 11.

## External links[edit | edit source]

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