# Pentagrammic-hexagonal duoprism

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Pentagrammic-hexagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Stahdip |

Coxeter diagram | x5/2o x6o () |

Elements | |

Cells | 6 pentagrammic prisms, 5 hexagonal prisms |

Faces | 30 squares, 6 pentagrams, 5 hexagons |

Edges | 30+30 |

Vertices | 30 |

Vertex figure | Digonal disphenoid, edge lengths (√5–1)/2 (base 1), √3 (base 2), √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Stip–5/2–stip: 120° |

Stip–4–hip: 90° | |

Hip–6–hip: 36° | |

Central density | 2 |

Number of external pieces | 16 |

Level of complexity | 12 |

Related polytopes | |

Army | Semi-uniform phiddip |

Regiment | Stahdip |

Dual | Pentagrammic-hexagonal duotegum |

Conjugate | Pentagonal-hexagonal duoprism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{2}×G_{2}, order 120 |

Convex | No |

Nature | Tame |

The **pentagrammic-hexagonal duoprism**, also known as **stahdip** or the **5/2-6 duoprism**, is a uniform duoprism that consists of 6 pentagrammic prisms and 5 hexagonal prisms, with 2 of each at each vertex.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A pentagrammic-hexagonal duoprism has the following Coxeter diagrams:

- x5/2o x6o (full symmetry)
- x3x x5/2o () (A
_{2}×H_{2}symmetry, hexagons as ditrigons)

## External links[edit | edit source]

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

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