# Pentagonal duoprism

The **pentagonal duoprism** or **pedip**, also known as the **pentagonal-pentagonal duoprism**, the **5 duoprism** or the **5-5 duoprism**, is a noble uniform duoprism that consists of 10 pentagonal prisms, with 4 meeting at each vertex. It is also the 10-4 gyrochoron and the square funk prism. It is the first in an infinite family of isogonal pentagonal dihedral swirlchora and also the first in an infinite family of isochoric pentagonal hosohedral swirlchora.

Pentagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Pedip |

Coxeter diagram | x5o x5o () |

Elements | |

Cells | 10 pentagonal prisms |

Faces | 25 squares, 10 pentagons |

Edges | 50 |

Vertices | 25 |

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

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dichoral angles | Pip–5–pip: 108° |

Pip–4–pip: 90° | |

Central density | 1 |

Number of external pieces | 10 |

Level of complexity | 3 |

Related polytopes | |

Army | Pedip |

Regiment | Pedip |

Dual | Pentagonal duotegum |

Conjugate | Pentagrammic duoprism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{2}≀S_{2}, order 200 |

Convex | Yes |

Nature | Tame |

A pentagonal duoprism of edge length 1 contains the vertices of a regular pentachoron of edge length , due to the fact the pentachoron is also the 5-2 step prism.

## GalleryEdit

## Vertex coordinatesEdit

The vertices of a pentagonal duoprism of edge length 1, centered at the origin, are given by:

## RepresentationsEdit

A pentagonal duoprism has the following Coxeter diagrams:

- x5o x5o (full symmetry)
- ofx xxx5ooo&#xt (pentagonal axial)

## External linksEdit

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

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

- Klitzing, Richard. "pedip".

- Wikipedia Contributors. "5-5 duoprism".

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