# Augmented tridiminished icosahedron

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Augmented tridiminished icosahedron | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Auteddi |

Coxeter diagram | oxfo3ooox&#xt |

Elements | |

Faces | 1+3+3 triangles, 3 pentagons |

Edges | 3+3+3+3+6 |

Vertices | 1+3+3+3 |

Vertex figures | 1 triangle, edge length 1 |

3 isosceles trapezoids, edge length 1, 1, 1, (1+√5)/2 | |

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

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

Measures (edge length 1) | |

Volume | |

Dihedral angles | 3–5 join: |

3–3 teddi: | |

3–5 teddi: | |

3–3 pyramidal: | |

5–5: | |

Central density | 1 |

Number of external pieces | 10 |

Level of complexity | 12 |

Related polytopes | |

Army | Auteddi |

Regiment | Auteddi |

Dual | Base-truncated tristellated dodecahedron |

Conjugates | Augmented trireplenished great icosahedron, Excavated trireplenished great icosahedron |

Abstract & topological properties | |

Flag count | 72 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | A_{2}×I, order 6 |

Convex | Yes |

Nature | Tame |

The **augmented tridiminished icosahedron** is one of the 92 Johnson solids (J_{64}). It consists of 1+3+3 triangles and 3 pentagons. It can be constructed by attaching a tetrahedron, seen as a triangular pyramid, to the triangular face of the tridiminished icosahedron that is connected only to pentagons.

It is the only Johnson solid that is constructed using both diminishing and augmenting, assuming that no diminishing and augmenting cancel each other out.

## Vertex coordinates[edit | edit source]

An augmented tridiminished icosahedron of edge length 1 has the following vertices:

Alternatively, orienting it so that it is derived from the vertices of a regular icosahedron, we obtain:

## External links[edit | edit source]

- Klitzing, Richard. "auteddi".
- Quickfur. "The Augmented Tridiminished Icosahedron".

- Wikipedia contributors. "Augmented tridiminished icosahedron".
- McCooey, David. "Augmented tridiminished Icosahedron"