# Small 12-5 double step prism

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

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

Rank | 4 |

Type | Isogonal |

Elements | |

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

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

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

Vertices | 24 |

Vertex figure | 11-vertex polyhedron with 18 triangular faces |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Small 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 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 48 irregular tetrahedra. 2 tetragonal disphenoid, 4 rhombic disphenoids, 4 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.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.70166.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a small 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* = √7-2√7+√33-12√7/4, *b* = √7+2√7+√33+12√7/4 and *k* is an integer from 0 to 11.

## External links[edit | edit source]

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