# Triangular-antitegmatic icosachoron

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Triangular-antitegmatic icosachoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Coxeter diagram | m3o3o3m () |

Elements | |

Cells | 20 triangular antitegums |

Faces | 60 rhombi |

Edges | 30+40 |

Vertices | 10+20 |

Vertex figure | 20 triangular bipyramids, 10 tetrahedra |

Measures (edge length 1) | |

Inradius | |

Dichoral angle | 120° |

Central density | 1 |

Related polytopes | |

Dual | Small prismatodecachoron |

Abstract & topological properties | |

Flag count | 960 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{4}×2, order 240 |

Convex | Yes |

Nature | Tame |

The **triangular-antitegmatic icosachoron** is a convex isochoric polychoron with 20 triangular antitegums as cells It can be obtained as the dual of the small prismatodecachoron.

It can also be constructed as the convex hull of 2 dual pentachora and 2 opposite rectified pentachora, all of the same edge length. Related to this fact is that it is the 4D vertex-first projection of the regular 5-cube, or in other words, it is the Minkowski sum of 5 line segments from the center to vertices of a pentachoron. This makes it a zonochoron.

Each face of this polyhedron is a rhombus with acute angle and obtuse angle .

## Isogonal derivatives[edit | edit source]

Substitution by vertices of these following elements will produce these convex isogonal polychora:

- Triangular antitegum (20): Small prismatodecachoron
- Rhombus (60): Rectified small prismatodecachoron
- Edge (30): Decachoron
- Edge (40): Bitruncatodecachoron
- Vertex (10): Bidecachoron
- Vertex (20): Biambodecachoron

## External links[edit | edit source]

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

- Klitzing, Richard. "m3o3o3m".