# Triangular-hexagonal duoprism

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Triangular-hexagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Thiddip |

Coxeter diagram | x3o x6o () |

Elements | |

Cells | 6 triangular prisms, 3 hexagonal prisms |

Faces | 6 triangles, 18 squares, 3 hexagons |

Edges | 18+18 |

Vertices | 18 |

Vertex figure | Digonal disphenoid, edge lengths 1 (base 1), √3 (base 2), and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Trip–3–trip: 120° |

Trip–4–hip: 90° | |

Hip–6–hip: 60° | |

Height | |

Central density | 1 |

Number of external pieces | 9 |

Level of complexity | 6 |

Related polytopes | |

Army | Thiddip |

Regiment | Thiddip |

Dual | Triangular-hexagonal duotegum |

Conjugate | None |

Abstract & topological properties | |

Flag count | 432 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{2}×G_{2}, order 72 |

Flag orbits | 6 |

Convex | Yes |

Nature | Tame |

The **triangular-hexagonal duoprism** or **thiddip**, also known as the **3-6 duoprism**, is a uniform duoprism that consists of 3 hexagonal prisms and 6 triangular prisms, with two of each meeting at each vertex.

The convex hull of two orthogonal triangular-hexagonal duoprisms is either the triangular duoexpandoprism or the triangular duotruncatoprism.

It is also a CRF segmentochoron, being a hexagon atop hexagonal prism. It is designated K-4.47 on Richard Klitzing's list.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

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

- ,
- ,
- ,
- .

## Representations[edit | edit source]

A triangular-hexagonal duoprism has the following Coxeter diagrams:

- x3o x6o () (full symmetry)
- x3x x3o () (A
_{2}×A_{2}symmetry, hexagon as ditrigon) - s3s2x3x ()
- ox xx6oo&#x (G
_{2}×A_{1}axial, hexagon atop hexagonal prism) - ox xx3xx&#x (A
_{2}×A_{1}axial, as above with ditrigon symmetry) - xux xxx3ooo&#x (A
_{2}×A_{1}axial, triangular prism-first)

## External links[edit | edit source]

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

- Klitzing, Richard. "Thiddip".
- Wikipedia contributors. "3-6 duoprism".