# Triangular-square duoprism

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

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Tisdip |

Coxeter diagram | x3o x4o () |

Tapertopic notation | 1^{1}11 |

Elements | |

Cells | 4 triangular prisms, 3 cubes |

Faces | 4 triangles, 3+12 squares |

Edges | 12+12 |

Vertices | 12 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Trip–4–cube: 90° |

Trip–3–trip: 90° | |

Cube–4–cube: 60° | |

Heights | Square atop cube: |

Trip atop trip: 1 | |

Central density | 1 |

Number of external pieces | 7 |

Level of complexity | 6 |

Related polytopes | |

Army | Tisdip |

Regiment | Tisdip |

Dual | Triangular-square duotegum |

Conjugate | None |

Abstract & topological properties | |

Flag count | 288 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{2}×B_{2}, order 48 |

Flag orbits | 6 |

Convex | Yes |

Nature | Tame |

The **triangular-square duoprism** or **tisdip**, also known as the **3-4 duoprism**, is a uniform duoprism that consists of 3 cubes and 4 triangular prisms, with two of each meeting at each vertex. It can also be seen as a prism based on the triangular prism, which makes it a convex segmentochoron (designated K-4.18 on Richard Klitzing's list) in two different ways, as a prism of a triangular prism or square atop cube.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

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

- ,
- .

## Representations[edit | edit source]

A triangular-square duoprism has the following Coxeter diagrams:

- x3o x4o () (full symmetry)
- x x x3o () (A
_{2}×A_{1}×A_{1}symmetry, triangular prismatic prism) - xx xx3oo&#x (A
_{2}×A_{1}axial, prism of triangular prism) - ox xx4oo&#x (B
_{2}×A_{1}axial, square atop cube) - ox xx xx&#x (K
_{3}symmetry, as above with rectangles instead of squares) - xxx3ooo oqo&#xt (A
_{2}×A_{1}axial, triangle-first) - xxx xxx&#x (A
_{1}×A_{1}symmetry, 3 squares seen separately)

## External links[edit | edit source]

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

- Klitzing, Richard. "tisdip".
- Quickfur. "The 3,4-Duoprism".

- Wikipedia contributors. "3-4 duoprism".