# Digonal-scalenohedral 8-3 double step prism

The **digonal-scalenohedral 8-3 double step prism** is a convex isogonal polychoron, formed as a convex hull of two 8-3 step prisms in a way that leaves six corealmic vertices corresponding to a digonal scalenohedron. It consists of 8 chiral digonal scalenohedra, 16 tetragonal disphenoids, and 16 phyllic disphenoids. 3 digonal scalenohedra, 4 tetragonal disphenoids, and 4 phyllic disphenoids join at each vertex.

Digonal-scalenohedral 8-3 double step prism | |
---|---|

File:Digonal-scalenohedral 8-3 double step prism.png | |

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 16 phyllic disphenoids, 16 tetragonal disphenoids, 8 chiral digonal scalenohedra |

Faces | 32 scalene triangles, 32+32 isosceles triangles |

Edges | 8+16+16+32 |

Vertices | 16 |

Vertex figure | 9-vertex polyhedron with 3 tetragons and 8 triangles |

Measures (based on unit rectified tesseract) | |

Edge lengths | 6-valence (16): 1 |

4-valence (16): | |

4-valence (8): | |

3-valence (32): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Dual | Trapezoprismatic intersected 8-3 bigyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(8)-3)×2R, order 32 |

Convex | Yes |

Nature | Tame |

It can be constructed by removing an inscribed digonal-scalenohedral 8-3 double step prism from a rectified tesseract.

The ratio between the longest and shortest edges is 1: ≈ 1:1.73205.

## Vertex coordinates edit

Coordinates for the vertices of a digonal-scalenohedral 8-3 double step prism are given by:

- (
*a**sin(2π*k*/8),*a**cos(2π*k*/8),*b**sin(6π*k*/8),*b**cos(6π*k*/8)), - (
*b**sin(2π*k*/8),*b**cos(2π*k*/8),*a**sin(6π*k*/8),*a**cos(6π*k*/8)),

where *a* = , *b* = , and *k* is an integer from 0 to 7.

## External links edit

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