# Augmented hexagonal prism

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Augmented hexagonal prism | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Auhip |

Coxeter diagram | oxxx oxux&#xt |

Elements | |

Faces | 2+2 triangles, 1+2+2 squares, 2 hexagons |

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

Vertices | 1+4+4+4 |

Vertex figures | 1 square, edge length 1 |

4 irregular tetragons, edge lengths 1, 1, √2, √3 | |

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

Measures (edge length 1) | |

Volume | |

Dihedral angles | 3–4: |

3–6: | |

4–4: 120° | |

3–3: | |

4–6: 90° | |

Central density | 1 |

Number of external pieces | 11 |

Level of complexity | 22 |

Related polytopes | |

Army | Auhip |

Regiment | Auhip |

Dual | Lateromonotruncated hexagonal tegum |

Conjugate | Augmented hexagonal prism |

Abstract & topological properties | |

Flag count | 88 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | K_{2}×I, order 4 |

Convex | Yes |

Nature | Tame |

The **augmented hexagonal prism** is one of the 92 Johnson solids (J_{54}). It consists of 2+2 triangles, 1+2+2 squares, and 2 hexagons. It can be constructed by attaching a square pyramid to one of the square faces of the hexagonal prism.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Klitzing, Richard. "auhip".
- Quickfur. "The Augmented Hexagonal Prism".

- Wikipedia contributors. "Augmented hexagonal prism".
- McCooey, David. "Augmented Hexagonal Prism"