# Great triakis icosahedron

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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 |

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

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 coordinates[edit | edit source]

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

## External links[edit | edit source]

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