# Tridyakis icosahedron

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Tridyakis icosahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Notation | |

Coxeter diagram | m5/3m3m5*a |

Elements | |

Faces | 120 scalene triangles |

Edges | 60+60+60 |

Vertices | 12+12+20 |

Vertex figure | 20 hexagons, 12 decagons, 12 decagrams |

Measures (edge length 1) | |

Inradius | |

Dihedral angle | |

Central density | 4 |

Number of external pieces | 240 |

Related polytopes | |

Dual | Icosidodecatruncated icosidodecahedron |

Conjugate | Tridyakis icosahedron |

Convex core | Non-Catalan disdyakis triacontahedron |

Abstract & topological properties | |

Flag count | 720 |

Euler characteristic | –16 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **tridyakis icosahedron** is a uniform dual polyhedron. It consists of 120 scalene triangles.

If its dual, the great cubicuboctahedron, has an edge length of 1, then the triangle faces' short edges will be , the medium edges will be , and the long edges will be . The triangles have one interior angle of , one of , and one of .

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Wikipedia contributors. "Tridyakis icosahedron".
- McCooey, David. "Tridyakis Icosahedron"