# Triangular-pentagonal duoprism

(Redirected from 5-3 duoprism)

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

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Trapedip |

Info | |

Coxeter diagram | x3o x5o |

Symmetry | A_{2}×H_{2}, order 60 |

Army | Trapedip |

Regiment | Trapedip |

Elements | |

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

Cells | 5 triangular prisms, 3 pentagonal prisms |

Faces | 5 triangles, 15 squares, 3 pentagons |

Edges | 15+15 |

Vertices | 15 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Trip–3–trip: 108° |

Trip–4–pip: 90° | |

Pip–5–pip: 60° | |

Height | |

Central density | 1 |

Euler characteristic | 0 |

Number of pieces | 8 |

Level of complexity | 6 |

Related polytopes | |

Dual | Triangular-pentagonal duotegum |

Conjugate | Triangular-pentagrammic duoprism |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **triangular-pentagonal duoprism** or **trapedip**, also known as the **3-5 duoprism**, is a uniform duoprism that consists of 3 pentagonal prisms and 5 triangular prisms, with two of each at each vertex.

It is also a CRF segmentochoron, as pentagon atop pentagonal prism. It is designated K-4.34 on Richard Klitzing's list.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a triangular-pentagonal duoprism with edge length 1 are given by:

## Representations[edit | edit source]

A triangular-pentagonal duoprism has the following Coxeter diagrams:

- x3o x5o (full symmetry)
- ox xx5oo&#x (pentagon atop pentagon prism)
- ofx xxx3oooo&#xt (triangle-first)

## External links[edit | edit source]

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

- Klitzing, Richard. "Trapedip".

- Wikipedia Contributors. "3-5 duoprism".