# Great triambic icosahedron

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Great triambic icosahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Notation | |

Bowers style acronym | Gatai |

Coxeter diagram | m3/2o3o5*a () |

Elements | |

Faces | 20 triambuses |

Edges | 60 |

Vertices | 20+12 |

Vertex figure | 20 triangles, 12 pentagons |

Measures (edge length 1) | |

Inradius | |

Volume | |

Surface area | |

Dihedral angle | |

Central density | 6 |

Number of external pieces | 60 |

Related polytopes | |

Dual | Great ditrigonary icosidodecahedron |

Conjugate | Small triambic icosahedron |

Abstract & topological properties | |

Flag count | 240 |

Euler characteristic | –8 |

Orientable | Yes |

Genus | 5 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **great triambic icosahedron** is a uniform dual polyhedron. It consists of 20 irregular hexagons, more specifically equilateral triambuses.

It appears the same as the medial triambic icosahedron.

If its dual, the great ditrigonary icosidodecahedron, has an edge length of 1, then the edges of the hexagons will measure . The hexagons have alternating interior angles of , and .

## Vertex coordinates[edit | edit source]

A great triambic icosahedron with dual edge length 1 has vertex coordinates given by all even permutations of:

## External links[edit | edit source]

- Klitzing, Richard. "gidtid".

- Wikipedia contributors. "Great triambic icosahedron".
- McCooey, David. "Great Triambic Icosahedron"