# Hexagonal duoprism

Hexagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Hiddip |

Coxeter diagram | x6o x6o () |

Elements | |

Cells | 12 hexagonal prisms |

Faces | 36 squares, 12 hexagons |

Edges | 72 |

Vertices | 36 |

Vertex figure | Tetragonal disphenoid, edge lengths √3 (base) and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dichoral angles | Hip–6–hip: 120° |

Hip–4–hip: 90° | |

Central density | 1 |

Number of external pieces | 12 |

Level of complexity | 3 |

Related polytopes | |

Army | Hiddip |

Regiment | Hiddip |

Dual | Hexagonal duotegum |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}≀S_{2}, order 288 |

Convex | Yes |

Nature | Tame |

The **hexagonal duoprism** or **hiddip**, also known as the **hexagonal-hexagonal duoprism**, the **6 duoprism** or the **6-6 duoprism**, is a noble uniform duoprism that consists of 12 hexagonal prisms, with 4 joining at each vertex. It is also the 12-5 gyrochoron. It is the first in an infinite family of isogonal hexagonal dihedral swirlchora and also the first in an infinite family of isochoric hexagonal hosohedral swirlchora.

This polychoron can be alternated into a triangular duoantiprism, although it cannot be made uniform.

A unit hexagonal duoprism can be vertex-inscribed into the antifrustary distetracontoctachoron and ditetrahedronary dishecatonicosachoron.

## Gallery[edit | edit source]

Wireframe, cell, net

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a hexagonal duoprism of edge length 1, centered at the origin, are given by:

## Representations[edit | edit source]

A hexagonal duoprism has the following Coxeter diagrams:

- x6o x6o (full symmetry)
- x3x x6o (one hexagon seen as ditrigon)
- x3x x3x (both hexagons seen as ditrigons, triangular duoprismatic symmetry)
- xux xxx6ooo&#xt (hexagonal axial)
- xux xxx3xxx&#xt (ditrigonal axial)

## External links[edit | edit source]

- Bowers, Jonathan. "Category A: Duoprisms".

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

- Klitzing, Richard. "hiddip".

- Wikipedia Contributors. "6-6 duoprism".

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