# 10-2 double step prism

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10-2 double step prism | |
---|---|

File:10-2 double step prism.png | |

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 40 phyllic disphenoids, 20 rhombic disphenoids, 20 tetragonal disphenoids |

Faces | 80 scalene triangles, 80 isosceles triangles |

Edges | 20+40+40 |

Vertices | 20 |

Vertex figure | Tetrakis parallelogramic alterprism |

Measures (longest edge length 1) | |

Edge lengths | 6-valence (40): |

4-valence (40): | |

4-valence (20): 1 | |

Central density | 1 |

Related polytopes | |

Dual | 10-2 bigyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(10)×2-2)×2I, order 80 |

Convex | Yes |

Nature | Tame |

The **10-2 double step prism** is a convex isogonal polychoron that consists of 20 tetragonal disphenoids, 20 rhombic disphenoids, and 40 phyllic disphenoids. 4 tetragonal disphenoids, 4 rhombic disphenoids, and 8 phyllic disphenoids join at each vertex. It can be obtained as the convex hull of two opposite 10-2 step prisms.

The ratio between the longest and shortest edges is 1: \approx 1:1.50588.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 10-2 double step prism are given by:

- ,
- ,

where *a* = 1/2 and *k* is an integer from 0 to 9.

## External links[edit | edit source]

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