# Tetragonal-antiwedge difold tritetraswirlchoron

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Tetragonal-antiwedge difold tritetraswirlchoron | |
---|---|

File:Tetragonal-antiwedge difold tritetraswirlchoron.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 24 phyllic disphenoids, 24 tetragonal antiwedges |

Faces | 24+24 isosceles triangles, 48 scalene triangles, 24 isosceles trapezoids |

Edges | 24+24+24+24 |

Vertices | 24 |

Vertex figure | Digonal-rectangular notch |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Tetragonal-antiwedge intersected tritetraswirlic icositetrachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A3+×4, order 48 |

Convex | Yes |

Nature | Tame |

The **tetragonal-antiwedge difold tritetraswirlchoron** is a convex isogonal polychoron that consists of 24 tetragonal antiwedges and 24 phyllic disphenoids. 6 tetragonal antiwedges and 4 phyllic disphenoids join at each vertex. It can be obtained as the convex hull of three hexadecachora or two orthogonal 12-5 step prisms.

The ratio between the longest and shortest edges is 1: ≈ 1:1.84776.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a tetragonal-antiwedge difold tritetraswirlchoron are given by:

- (
*a**sin(2π*k*/12),*a**cos(2π*k*/12),*b**sin(10π*k*/12),*b**cos(10π*k*/12)), - (
*b**sin(2π*k*/12),*b**cos(2π*k*/12),*a**sin(10π*k*/12),*a**cos(10π*k*/12)),

where *a* = √18-6√3/6, *b* = √18+6√3/6 and *k* is an integer from 0 to 11.

## External links[edit | edit source]

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