# Augmented pentagonal prism

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Augmented pentagonal prism | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Aupip |

Coxeter diagram | oxxx oxfo&#xt |

Elements | |

Faces | 2+2 triangles, 2+2 squares, 2 pentagons |

Edges | 1+2+2+2+4+4+4 |

Vertices | 1+2+4+4 |

Vertex figures | 1 square, edge length 1 |

4 irregular tetragons, edge lengths 1, 1, √2, (1+√5)/2 | |

2+4 isosceles triangles, edge lengths (1+√5)/2, √2, √2 | |

Measures (edge length 1) | |

Volume | |

Dihedral angles | 3–4 join: |

3–5 join: | |

3–3 pyramidal: | |

4–4: 108° | |

4–5: 90° | |

Central density | 1 |

Number of external pieces | 10 |

Level of complexity | 19 |

Related polytopes | |

Army | Aupip |

Regiment | Aupip |

Dual | Lateromonotruncated pentagonal tegum |

Conjugates | Augmented pentagrammic prism, Excavated pentagonal prism, Excavated pentagrammic prism |

Abstract & topological properties | |

Flag count | 76 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | K_{2}×I, order 4 |

Convex | Yes |

Nature | Tame |

The **augmented pentagonal prism** is one of the 92 Johnson solids (J_{52}). It consists of 2+2 triangles, 2 +2squares, and 2 pentagons. It can be constructed by attaching a square pyramid to one of the square faces of the pentagonal prism.

## Vertex coordinates[edit | edit source]

An augmented pentagonal prism of edge length 1 has the following vertices:

## External links[edit | edit source]

- Klitzing, Richard. "aupip".
- Quickfur. "The Augmented Pentagonal Prism".

- Wikipedia contributors. "Augmented pentagonal prism".
- McCooey, David. "Augmented Pentagonal Prism"