# Hexagonal duotegum

(Redirected from 12-5 step prism)

Hexagonal duotegum | |
---|---|

Rank | 4 |

Type | Noble |

Notation | |

Bowers style acronym | Hiddit |

Coxeter diagram | m6o2m6o () |

Elements | |

Cells | 36 tetragonal disphenoids |

Faces | 72 isosceles triangles |

Edges | 12+36 |

Vertices | 12 |

Vertex figure | Hexagonal tegum |

Measures (based on hexagons of edge length 1) | |

Edge lengths | Base (12): 1 |

Lacing (36): | |

Circumradius | 1 |

Inradius | |

Central density | 1 |

Related polytopes | |

Army | Hiddit |

Regiment | Hiddit |

Dual | Hexagonal duoprism |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}≀S_{2}, order 288 |

Convex | Yes |

Nature | Tame |

The **hexagonal duotegum** or **hiddit**, also known as the **hexagonal-hexagonal duotegum**, the **6 duotegum**, or the **6-6 duotegum**, is a noble duotegum that consists of 36 tetragonal disphenoids and 12 vertices, with 12 cells joining at each vertex. It is also the 12-5 step prism. It is the first in an infinite family of isogonal hexagonal hosohedral swirlchora and also the first in an infinite family of isochoric hexagonal dihedral swirlchora.

The ratio between the longest and shortest edges is 1: ≈ 1:1.41421.

## Vertex coordinates[edit | edit source]

The vertices of a hexagonal duotegum based on two hexagons of edge length 1, centered at the origin, are given by:

- ,
- ,
- ,
- .