# Bidodecateron

Bidodecateron | |
---|---|

File:Bidodecateron.png | |

Rank | 5 |

Type | Noble |

Notation | |

Bowers style acronym | Bidot |

Coxeter diagram | o3o3m3o3o () |

Elements | |

Tera | 20 triangular duotegums |

Cells | 90 tetragonal disphenoids |

Faces | 120 isosceles triangles |

Edges | 30+30 |

Vertices | 12 |

Vertex figure | Joined pentachoron |

Measures (based on 2 5-simplices of edge length 1) | |

Edge lengths | Lacing edges (30): |

Base edges (30): 1 | |

Circumradius | |

Inradius | |

Diteral angle | |

Height | |

Central density | 1 |

Related polytopes | |

Army | Bidot |

Regiment | Bidot |

Dual | Dodecateron |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{5}×2, order 1440 |

Convex | Yes |

Nature | Tame |

The **bidodecateron** or **bidot**, also known as the **triangular-duotegmatic icosateron** or **triangular duotegmatic alterprism**, is a convex noble polyteron with 20 identical triangular duotegums as facets. 10 facets join at each vertex, with the vertex figure being a joined pentachoron. It can be obtained as the convex hull of a hexateron and its central inversion (or, equivalently, its dual). It is also the triangular member of an infinite series of isogonal duotegmatic alterprisms.

The ratio between the longest and shortest edges is .

## Vertex coordinates[edit | edit source]

The vertices of a bidodecateron, based on two hexatera of edge length 1, centered at the origin, are given by:

- ,
- ,
- ,
- ,
- .

## External links[edit | edit source]

- Klitzing, Richard. "bidot".