# Augmented dodecahedron (Johnson solid)

Jump to navigation
Jump to search

Augmented dodecahedron (Johnson solid) | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Aud |

Coxeter diagram | oxfoo ooofx&#xt |

Stewart notation | J_{58} |

Elements | |

Faces | 5 triangles, 1+5+5 pentagons |

Edges | 5+5+5+5+5+10 |

Vertices | 1+5+5+5+5 |

Vertex figures | 1 pentagon, edge length 1 |

5 kites, edge lengths 1 and (1+√5)/2 | |

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

Measures (edge length 1) | |

Volume | |

Dihedral angles | 3–5: |

3–3: | |

5–5: | |

Central density | 1 |

Number of external pieces | 16 |

Level of complexity | 14 |

Related polytopes | |

Army | Aud |

Regiment | Aud |

Dual | Monotruncated icosahedron |

Conjugate | Monoexcavated great stellated dodecahedron |

Abstract & topological properties | |

Flag count | 140 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{2}×I, order 10 |

Convex | Yes |

Nature | Tame |

The **augmented dodecahedron** is one of the 92 Johnson solids (J_{58}). It consists of 5 triangles and 1+5+5 pentagons. It can be constructed by attaching a pentagonal pyramid to one of the faces of the regular dodecahedron.

## Vertex coordinates[edit | edit source]

An augmented dodecahedron of edge length 1 has vertices given by all even permutations of:

- ,

As well as:

- ,
- .

## External links[edit | edit source]

- Klitzing, Richard. "aud".
- Quickfur. "The Augmented Dodecahedron".

- Wikipedia contributors. "Augmented dodecahedron".
- McCooey, David. "Augmented Dodecahedron"