# Great 12-5 double step prism

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Great 12-5 double step prism | |
---|---|

File:Great 12-5 double step prism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 12 tetragonal disphenoids, 12+12 rhombic disphenoids, 24 phyllic disphenoids, 48+48 irregular tetrahedra |

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

Edges | 12+24+24+24+24+24+48 |

Vertices | 24 |

Vertex figure | 15-vertex polyhedron with 26 triangular faces |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Great 12-5 bigyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I2(12)+×4×I, order 48 |

Convex | Yes |

Nature | Tame |

The **great 12-5 double step prism** is a convex isogonal polychoron that consists of 12 tetragonal disphenoids, 24 rhombic disphenoids of two kinds, 24 phyllic disphenoids, and 96 irregular tetrahedra of two kinds. 2 tetragonal disphenoids, 4 rhombic disphenoids, 4 phyllic disphenoids, and 16 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* = √33+12√7/3) would yield a small 12-5 double step prism instead.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a great 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*/*b* is greater than 7-4√3 but less than 2-√3 and *k* is an integer from 0 to 11.

## External links[edit | edit source]

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