# Great triakis icosahedron

The **great triakis icosahedron** is a uniform dual polyhedron. It consists of 60 isosceles triangles.

Great triakis icosahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Coxeter diagram | m5/3m3o |

Elements | |

Faces | 60 isosceles triangles |

Edges | 30+60 |

Vertices | 20+12 |

Vertex figure | 20 triangles, 12 decagrams |

Measures (edge length 1) | |

Inradius | |

Dihedral angle | |

Central density | 13 |

Number of external pieces | 420 |

Related polytopes | |

Dual | Quasitruncated great stellated dodecahedron |

Abstract & topological properties | |

Flag count | 360 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

If its dual, the quasitruncated great stellated dodecahedron, has an edge length of 1, then the short edges of the triangles will measure , and the long edges will be . The triangles have two interior angles of , and one of .

## Vertex coordinatesEdit

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

## External linksEdit

- Wikipedia Contributors. "Great triakis icosahedron".
- McCooey, David. "Great Triakis Icosahedron"