# Great 10-3 double step prism

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Great 10-3 double step prism | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

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

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

Edges | 10+20+20+40+40 |

Vertices | 20 |

Vertex figure | 13-vertex polyhedron with 22 triangular faces |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Great 10-3 bigyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I2(10)+×4×I, order 40 |

Convex | Yes |

Nature | Tame |

The **great 10-3 double step prism** is a convex isogonal polychoron that consists of 10 tetragonal disphenoids, 20 phyllic disphenoids, and 80 irregular tetrahedra of two kinds. 2 tetragonal disphenoids, 4 phyllic disphenoids, and 16 irregular tetrahedra join at each vertex. I t can be obtained as one of several polychora formed 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* = (3-√5)/2) would yield a biambodecachoron instead.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a great 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*/*b* is greater than but less than and *k* is an integer from 0 to 9.

## External links[edit | edit source]

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