# Triangular-decagonal duoprism

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

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Tradedip |

Coxeter diagram | x3o x10o () |

Elements | |

Cells | 10 triangular prisms, 3 decagonal prisms |

Faces | 10 triangles, 30 squares, 3 decagons |

Edges | 30+30 |

Vertices | 30 |

Vertex figure | Digonal disphenoid, edge lengths 1 (base 1), √(5+√5)/2 (base 2), and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Trip–3–trip: 144° |

Trip–4–dip: 90° | |

Dip–10–dip: 60° | |

Height | |

Central density | 1 |

Number of external pieces | 13 |

Level of complexity | 6 |

Related polytopes | |

Army | Tradedip |

Regiment | Tradedip |

Dual | Triangular-decagonal duotegum |

Conjugate | Triangular-decagrammic duoprism |

Abstract & topological properties | |

Flag count | 720 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{2}×I_{2}(10), order 120 |

Flag orbits | 6 |

Convex | Yes |

Nature | Tame |

The **triangular-decagonal duoprism** or **tradedip**, also known as the **3-10 duoprism**, is a uniform duoprism that consists of 3 decagonal prisms and 10 triangular prisms, with 2 of each at each vertex.

It is also a CRF segmentochoron, being decagon atop decagonal prism. It is designated K-4.94 on Richard Klitzing's list.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

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

- ,
- ,
- ,
- ,
- ,
- .

## Representations[edit | edit source]

A triangular-decagonal duoprism has the following Coxeter diagrams:

- x3o x10o () (full symetry)
- x3o x5x () (A
_{2}×H_{2}symmetry, decagon as dipentagon) - ox xx10oo&#x (I
_{2}(10)×A_{1}axial, decagon atop decagon prism) - ox xx5xx&#x (H
_{2}×A_{1}axial)

## External links[edit | edit source]

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

- Klitzing, Richard. "tradedip".