# Transitional 10-3 double step prism

The **transitional 10-3 double step prism** is a convex isogonal polychoron that consists of 10 digonal scalenohedra, 20 rhombic disphenoids, and 40 phyllic disphenoids. 3 digonal scalenohedra, 4 rhombic disphenoids, and 8 phyllic disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal 10-3 step prisms.

Transitional 10-3 double step prism | |
---|---|

File:Transitional 10-3 double step prism.png | |

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 40 phyllic disphenoids, 20 rhombic disphenoids, 10 digonal scalenohedra |

Faces | 40+40+40+40 scalene triangles |

Edges | 10+20+40+40 |

Vertices | 20 |

Vertex figure | Polyhedron with 3 tetraogns and 12 triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Transitional 10-3 bigyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(10)-3)×2I, order 40 |

Convex | Yes |

Nature | Tame |

The ratio between the longest and shortest edges is 1: ≈ 1:2.23607.

## Vertex coordinates Edit

Coordinates for the vertices of a transitional 10-3 double step prism are given by:

- (
*a**sin(2π*k*/10),*a**cos(2π*k*/10),*b**sin(6π*k*/10),*b**cos(6π*k*/10)), - (
*b**sin(2π*k*/10),*b**cos(2π*k*/10),*a**sin(6π*k*/10),*a**cos(6π*k*/10)),

where *a* = √42-18√5/6, *b* = √42+18√5/6 and *k* is an integer from 0 to 9.

## External links Edit

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