# Pentagrammic duoprism

(Redirected from 5/2-5/2 duoprism)

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

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Stardip |

Info | |

Coxeter diagram | x5/2o x5/2o |

Symmetry | H2≀S2, order 200 |

Army | Pedip |

Regiment | Stardip |

Elements | |

Vertex figure | Tetragonal disphenoid, edge lengths (√5–1)/2 (bases) and √2 (sides) |

Cells | 10 pentagrammic prisms |

Faces | 25 squares, 10 pentagrams |

Edges | 50 |

Vertices | 25 |

Measures (edge length 1) | |

Circumradius | √(5–√5)/5 ≈ 0.74350 |

Inradius | √(5–2√5)/20 ≈ 0.16246 |

Hypervolume | 5(5–2√5)/16 ≈ 0.16496 |

Dichoral angles | Stip–5/2-stip: 36° |

Stip–4–stip: 90° | |

Central density | 4 |

Related polytopes | |

Dual | Pentagrammic duotegum |

Conjugate | Pentagonal duoprism |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **pentagrammic duoprism** or **stardip**, also known as the **pentagrammic-pentagrammic duoprism**, the **5/2 duoprism** or the **5/2-5/2 duoprism**, is a noble uniform duoprism that consists of 10 pentagrammic prisms and 25 vertices.

## Vertex coordinates[edit | edit source]

The coordinates of a pentagrammic duoprism of edge length 1, centered at the origin, are given by:

- (±1/2, –√(5–2√5)/20, ±1/2, –√(5–2√5)/20),
- (±1/2, –√(5–2√5)/20, ±(√5–1)/4, √(5+√5)/40),
- (±1/2, –√(5–2√5)/20, 0, –√(5–√5)/10),
- (±(√5–1)/4, √(5+√5)/40, ±1/2, –√(5–2√5)/20),
- (±(√5–1)/4, √(5+√5)/40, ±(√5–1)/4, √(5+√5)/40),
- (±(√5–1)/4, √(5+√5)/40, 0, –√(5–√5)/10),
- (0, –√(5–√5)/10, ±1/2, –√(5–2√5)/20),
- (0, –√(5–√5)/10, ±(√5–1)/4, √(5+√5)/40),
- (0, –√(5–√5)/10, 0, –√(5–√5)/10).

## External links[edit | edit source]

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

- Klitzing, Richard. "Stardip".

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