# 12-5 double gyrostep prism

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

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

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 24+24+24 phyllic disphenoids, 48 irregular tetrahedra |

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

Edges | 24+24+24+24+48 |

Vertices | 24 |

Vertex figure | 12-vertex polyhedron with 20 triangular faces |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | 12-5 antibigyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I2(12)+×4×I, order 48 |

Convex | Yes |

Nature | Tame |

The **12-5 double gyrostep prism** is a convex isogonal polychoron that consists of 12 tetragonal disphenoids, 24 rhombic disphenoids of two kinds, 24 phyllic disphenoids and 48 irregular tetrahedra. 12 phyllic disphenoids and 8 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 12-5 step prisms.

This polychoron cannot be optimized using the ratio method, because the solution (*a*/*b* = ) would yield a 24-5 step prism instead.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 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*/*b* is greater than √2-√3 but less than 2√3+√14-8√3-3 and *k* is an integer from 0 to 11.

## External links[edit | edit source]

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