# Triangular duoprism

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

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Triddip |

Coxeter diagram | x3o x3o () |

Tapertopic notation | 1^{1}1^{1} |

Elements | |

Cells | 6 triangular prisms |

Faces | 6 triangles, 9 squares |

Edges | 18 |

Vertices | 9 |

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

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dichoral angles | Trip–4–trip: 90° |

Trip–3–trip: 60° | |

Height | |

Central density | 1 |

Number of pieces | 6 |

Level of complexity | 3 |

Related polytopes | |

Army | Triddip |

Regiment | Triddip |

Dual | Triangular duotegum |

Conjugate | None |

Abstract properties | |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | A_{2}≀S_{2}, order 72 |

Convex | Yes |

Nature | Tame |

The **triangular duoprism** or **triddip**, also known as the **triangular-triangular duoprism**, the **3 duoprism** or the **3-3 duoprism**, is a noble uniform duoprism that consists of 6 triangular prisms, with 4 meeting at each vertex. It is the simplest possible duoprism (excluding the degenerate dichora) and is also the 6-2 gyrochoron. It is the first in an infinite family of isogonal triangular dihedral swirlchora and also the first in an infinite family of isochoric triangular hosohedral swirlchora.

It is also a convex segmentochoron (designated K-4.10 on Richard Klitzing's list), as it is a triangle atop a triangular prism.

## Gallery[edit | edit source]

Segmentochoron display, triangle atop triangular prism

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A triangular duoprism has the following Coxeter diagrams:

- x3o x3o (full symmetry)
- ox xx3oo&#x (axial, triangle atop triangular prism)
- xxoo xoox&#xr (axial, vertex first)
- xxx3ooo&#x (A2 axial)

## Related polychora[edit | edit source]

### Isogonal derivatives[edit | edit source]

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

- Triangular prism (6): Triangular duotegum
- Triangle (6): Triangular duotegum
- square (9): Triangular duoprism
- Edge (18): Rectified triangular duoprism

## External links[edit | edit source]

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

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

- Klitzing, Richard. "triddip".

- Quickfur. "The 3,3-Duoprism".

- Wikipedia Contributors. "3-3 duoprism".
- Hi.gher.Space Wiki Contributors. "Duotrianglinder".