# Pentagonal-dodecagonal duoprism

(Redirected from 5-12 duoprism)

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

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Pitwadip |

Info | |

Coxeter diagram | x5o x12o |

Symmetry | H2×I2(12), order 240 |

Army | Pitwadip |

Regiment | Pitwadip |

Elements | |

Vertex figure | Digonal disphenoid, edge lengths (1+√5)/2 (base 1), (√2+√6)/2 (base 2), and √2 (sides) |

Cells | 12 pentagonal prisms, 5 dodecagonal prisms |

Faces | 60 squares, 12 pentagons, 5 dodecagons, |

Edges | 60+60 |

Vertices | 60 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Twip–12–twip: 108° |

Pip–5–pip: 150° | |

Twip–4–pip: 90° | |

Central density | 1 |

Euler characteristic | 0 |

Number of pieces | 17 |

Level of complexity | 6 |

Related polytopes | |

Dual | Pentagonal-dodecagonal duotegum |

Conjugates | Pentagonal-dodecagrammic duoprism, Pentagrammic-dodecagonal duoprism, Pentagrammic-dodecagrammic duoprism |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **pentagonal-dodecagonal duoprism** or **pitwadip**, also known as the **5-12 duoprism**, is a uniform duoprism that consists of 5 dodecagonal prisms and 12 pentagonal prisms, with two of each joining at each vertex.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A pentagonal-dodecagonal duoprism has the following Coxeter diagrams:

- x5o x12o (full symmetry)
- x5o x6x (dodecagons as dihexagons)

## External links[edit | edit source]

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