# Disdyakis triacontahedron

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Disdyakis triacontahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Bowers style acronym | Siddykit |

Coxeter diagram | m5m3m () |

Conway notation | mD |

Elements | |

Faces | 120 scalene triangles |

Edges | 60+60+60 |

Vertices | 12+20+30 |

Vertex figure | 12 decagons, 20 hexagons, 30 squares |

Measures (edge length 1) | |

Dihedral angle | |

Central density | 1 |

Number of external pieces | 120 |

Level of complexity | 6 |

Related polytopes | |

Army | Siddykit |

Regiment | Siddykit |

Dual | Great rhombicosidodecahedron |

Conjugate | Great disdyakis triacontahedron |

Abstract & topological properties | |

Flag count | 720 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | Yes |

Nature | Tame |

The **disdyakis triacontahedron**, also called the **small disdyakis triacontahedron**, is one of the 13 Catalan solids. It has 120 scalene triangles as faces, with 12 order-10, 20 order-6, and 30 order-4 vertices. It is the dual of the uniform great rhombicosidodecahedron.

It can also be obtained as the convex hull of a dodecahedron, an icosahedron, and an icosidodecahedron. If the dodecahedron has unit edge length, the icosahedron's edge length is and the icosidodecahedron's edge length is .

Each face of this polyhedron is a scalene triangle. If the shortest edges have unit edge length, the medium edges have length and the longest edges have length . These triangles have angles measuring , , and .

## External links[edit | edit source]

- Wikipedia Contributors. "Disdyakis triacontahedron".
- McCooey, David. "Disdyakis Triacontahedron"