# Compound of two small icosicosidodecahedra

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Compound of two small icosicosidodecahedra | |
---|---|

Rank | 3 |

Type | Compound |

Elements | |

Components | 2 small icosicosidodecahedra |

Faces | 24 triangles, 24 pentagrams, 24 hexagons, 8 golden hexagrams, 8 compound of two hexagons |

Edges | 72+48+48+48+24 |

Vertices | 24+48+48 |

Vertex figure | Isosceles trapezoid, edge lengths 1, √3, (√5–1)/2, √3 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 5/2–6: |

3–6: | |

Central density | 4 |

Related polytopes | |

Regiment | Compound of two small icosicosidodecahedra |

Dual | Compound of two small icosacronic hexecontahedra |

Conjugate | Compound of two great icosicosidodecahedra |

Convex core | Octatruncated tetrakis hexahedron |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{3}, order 48 |

Convex | No |

Nature | Tame |

The **compound of two small icosicosidodecahedra** 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 40 hexagons (16 of which form 8 compound of two hexagons). One triangle, two hexagons, and one pentagram (sometimes a hexagram replaces the triangle, or one or more compounds of two hexagons replaces a hexagon) join at each vertex.

## Related polytopes[edit | edit source]

The compound of two small icosicosidodecahedra is one of the facets of some uniform polychora of the sadros 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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