# Compound of two great ditrigonal dodecicosidodecahedra

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Compound of two great ditrigonal dodecicosidodecahedra | |
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Rank | 3 |

Type | Compound |

Elements | |

Components | 2 great ditrigonal dodecicosidodecahedra |

Faces | 24 triangles, 24 pentagrams, 24 decagrams, 8 golden hexagrams |

Edges | 120+72+48 |

Vertices | 72+48 |

Vertex figure | Isosceles trapezoid, edge lengths 1, √(5–√5)/2, (1+√5)/2, √(5–√5)/2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 3–10/3: |

5–10/3: | |

Central density | 8 |

Related polytopes | |

Regiment | Compound of two great ditrigonal dodecicosidodecahedra |

Dual | Compound of two great ditrigonal dodecacronic hexecontahedra |

Conjugate | Compound of two small ditrigonal dodecicosidodecahedra |

Convex hull | Semi-uniform great rhombicuboctahedron augmented with square cupolas and ditrigonal frustums |

Convex core | Tetrakis hexahedron |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{3}, order 48 |

Convex | No |

Nature | Tame |

The **compound of two great ditrigonal dodecicosidodecahedra** is a polyhedron compound. It consists of 40 triangles (16 of which fall into pairs in the same planes, forming 8 golden hexagrams), 24 pentagrams, and 24 decagrams. One triangle, one pentagram, and two decagrams (sometimes a hexagram replaces the triangle) join at each vertex.

## Related polytopes[edit | edit source]

The compound of two great ditrigonal dodecicosidodecahedra is one of the facets of some uniform polychora of the gadros daskydox regiment.

Its non-standard hexagram faces are *not* to be confused with the hexagram faces of the small snub icosicosidodecahedron.

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