# 10-3 double gyrostep prism

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10-3 double gyrostep prism | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Info | |

Symmetry | I2(10)+×4×I, order 40 |

Elements | |

Cells | 10+10 tetragonal disphenoids, 20 phyllic disphenoids, 40 irregular tetrahedra |

Faces | 20+20 isosceles triangles, 40+40+40 scalene triangles |

Edges | 20+20+20+40 |

Vertices | 20 |

Central density | 1 |

Euler characteristic | 0 |

Related polytopes | |

Dual | 10-3 antibigyrochoron |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **10-3 double gyrostep prism** is a convex isogonal polychoron that consists of 20 tetragonal disphenoids of two kinds, 20 phyllic disphenoids and 40 irregular tetrahedra obtained as the convex hull of two orthogonal 10-3 step prisms.

This polychoron cannot be optimized using the ratio method, because the solution (*a*/*b* = (√5-1)/2) would yield a small prismatodecachoron instead.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 10-3 double gyrostep 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*/*b* is greater than √5-2 but less than (√5-1)/2 and *k* is an integer from 0 to 9.

## External links[edit | edit source]

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

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