# Dodecagonal-dodecagrammic duoprism

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Dodecagonal-dodecagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Coxeter diagram | x12o x12/5o () |

Elements | |

Cells | 12 dodecagonal prisms, 12 dodecagrammic prisms |

Faces | 144 squares, 12 dodecagons, 12 dodecagrams |

Edges | 144+144 |

Vertices | 144 |

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

Measures (edge length 1) | |

Circumradius | 2 |

Hypervolume | 9 |

Dichoral angles | Stwip–12/5–stwip: 150° |

Twip–4–stwip: 90° | |

Twip–12–twip: 30° | |

Central density | 5 |

Number of external pieces | 36 |

Level of complexity | 12 |

Related polytopes | |

Army | Semi-uniform twaddip |

Dual | Dodecagonal-dodecagrammic duotegum |

Conjugate | Dodecagonal-dodecagrammic duoprism |

Abstract & topological properties | |

Flag count | 3456 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(12)×I_{2}(12), order 576 |

Convex | No |

Nature | Tame |

The **dodecagonal-dodecagrammic duoprism**, also known as the **12/5-12 duoprism**, is a uniform duoprism that consists of 12 dodecagonal prisms and 12 dodecagrammic prisms, with 2 of each at each vertex.

## Vertex coordinates[edit | edit source]

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

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

## Representations[edit | edit source]

A dodecagonal-dodecagrammic duoprism has the following Coxeter diagrams:

- x12o x12/5o () (full symmetry)
- x6x x12/5o () (G
_{2}×I_{2}(12) symmetry, dodecagons as dihexagons) - x6/5x x12o () (G
_{2}×I_{2}(12) symmetry, dodecagrams as dihexagrams) - x6x x6/5x () (G
_{2}×G_{2}symmetry)

## External links[edit | edit source]

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

- Klitzing, Richard. "nd-mb-dip".