# Square-dodecagrammic duoprism

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Square-dodecagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Coxeter diagram | x4o2x12/5o () |

Elements | |

Cells | 12 cubes, 4 dodecagrammic prisms |

Faces | 12+48 squares, 4 dodecagrams |

Edges | 48+48 |

Vertices | 48 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Stwip–12/5–stwip: 90° |

Cube–4–stwip: 90° | |

Cube–4–cube: 30° | |

Height | 1 |

Central density | 5 |

Number of external pieces | 28 |

Level of complexity | 12 |

Related polytopes | |

Army | Semi-uniform sitwadip |

Dual | Square-dodecagrammic duotegum |

Conjugate | Square-dodecagonal duoprism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}×I_{2}(12), order 192 |

Convex | No |

Nature | Tame |

The **square-dodecagrammic duoprism**, also known as the **4-12/5 duoprism**, is a uniform duoprism that consists of 12 cubes and 4 dodecagrammic prisms, with 2 of each at each vertex.

## Vertex coordinates[edit | edit source]

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

- ,
- ,
- .

## Representations[edit | edit source]

A square-dodecagrammic duoprism has the following Coxeter diagrams:

- x4o x12/5o () (full symmetry)
- x x x12/5o () (I
_{2}(12)×A_{1}×A_{1}symmetry, dodecagrammic prismatic prism) - x4o x6/5x () (B
_{2}×G_{2}symmetry) - x x x6/5x () (G
_{2}×A_{1}×A_{1}symmetry)

## External links[edit | edit source]

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

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