# Pentagonal-pentagrammic duoprism

Pentagonal-pentagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Starpedip |

Coxeter diagram | x5o x5/2o () |

Elements | |

Cells | 5 pentagonal prisms, 5 pentagrammic prisms |

Faces | 25 squares, 5 pentagons, 5 pentagrams |

Edges | 25+25 |

Vertices | 25 |

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

Measures (edge length 1) | |

Circumradius | 1 |

Hypervolume | |

Dichoral angles | Stip–5/2–stip: 108° |

Pip–4–stip: 90° | |

Pip–5–pip: 36° | |

Central density | 2 |

Number of external pieces | 15 |

Level of complexity | 12 |

Related polytopes | |

Army | Semi-uniform pedip |

Regiment | Starpedip |

Dual | Pentagonal-pentagrammic duotegum |

Conjugate | Pentagonal-pentagrammic duoprism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{2}×H_{2}, order 100 |

Convex | No |

Nature | Tame |

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

This is the only duoprism aside from the tesseract to have a circumradius equal to its edge length. A consequence of this is that two opposite pentagonal-pentagrammic duoprisms can be vertex-inscribed into the great duoantiprism.

The pentagonal-pentagrammic duoprism can be edge-inscribed into the small stellated hecatonicosachoron. The small stellated hecatonicosachoron's regiment contains a uniform compound of 24 pentagonal-pentagrammic duoprisms.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

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

- Klitzing, Richard. "starpedip".