# Pentagonal-decagonal duoprism

(Redirected from 5-10 duoprism)

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

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Padedip |

Info | |

Coxeter diagram | x5o x10o |

Symmetry | H2×I2(10), order 200 |

Army | Padedip |

Regiment | Padedip |

Elements | |

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

Cells | 10 pentagonal prisms, 5 decagonal prisms |

Faces | 50 squares, 10 pentagons, 5 decagons |

Edges | 50+50 |

Vertices | 50 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Pip–5–pip: 144° |

Dip–5–dip: 108° | |

Dip–4–pip: 90° | |

Central density | 1 |

Euler characteristic | 0 |

Number of pieces | 15 |

Level of complexity | 6 |

Related polytopes | |

Dual | Pentagonal-decagonal duotegum |

Conjugates | Pentagonal-decagrammic duoprism, Pentagrammic-decagonal duoprism, Pentagrammic-decagrammic duoprism |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **pentagonal-decagonal duoprism** or **padedip**, also known as the **5-10 duoprism**, is a uniform duoprism that consists of 5 decagonal prisms and 10 pentagonal prisms, with two of each joining at each vertex.

The convex hull of two orthogonal pentagonal-decagonal duoprisms is either the pentagonal duoexpandoprism or the pentagonal duotruncatoprism.

## Vertex coordinates[edit | edit source]

The vertex coordinates of a pentagonal-decagonal duoprism, centered at the origin and with unit edge length, are given by:

## Representations[edit | edit source]

A pentagonal-decagonal duoprism has the following Coxeter diagrams:

- x5o x10o (full symmetry)
- x5x x5o (edcagons as dipentagons, pentagon duoprism symmetry)
- ofx xxx10ooo&#xt (decagonal axial)
- ofx xxx5xxx&#xt (dipentagonal axial symmetry)

## External links[edit | edit source]

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

- Klitzing, Richard. "Padedip".

- Quickfur. "The 5,10-Duoprism".