# Difold ditetraswirlchoron

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Difold ditetraswirlchoron | |
---|---|

200px | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Info | |

Symmetry | A3+×4, order 48 |

Elements | |

Vertex figure | 10-vertex polyhedron with 3 tetragons and 10 triangles |

Cells | 16 triangular pyramids, 24 phyllic disphenoids, 8 triangular antiprisms |

Faces | 16 triangles, 48 isosceles triangles, 48 scalene triangles |

Edges | 8+24+48 |

Vertices | 16 |

Measures (circumradius 1, based on a 2D regular dodecagonal envelope) | |

Edge lengths | 6-valence (8): |

6-valence (24): | |

3-valence (48): | |

Central density | 1 |

Euler characteristic | 0 |

Related polytopes | |

Dual | Ditetraswirlic hexadecachoron |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **difold ditetraswirlchoron**, also known as the **disphenoidal-digonal scalenohedral 8-3 double step prism**, is one of several isogonal polychoron, formed as a convex hull of two hexadecachora. It consists of 8 triangular antiprisms, 16 triangular pyramids, and 24 phyllic disphenoids. 3 triangular antiprisms, 4 triangular pyramids, and 6 phyllic disphenoids join at each vertex.

This polychoron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1: ≈ 1:1.41421) would yield a tesseract instead.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a difold ditetraswirlchoron based on a 2D regular dodecagonal envelope of circumradius 1, centered at the origin, are given by:

## External links[edit | edit source]

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