# Rhombic hexecontahedron

Rhombic hexecontahedron | |
---|---|

Rank | 3 |

Space | Spherical |

Elements | |

Faces | 60 golden rhombi |

Edges | 60 + 60 |

Vertices | 12 + 20 + 30 |

Measures (edge length 1) | |

Volume | |

Surface area | |

Central density | 1 |

Related polytopes | |

Convex hull | Dodecahedron |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

The **rhombic hexecontahedron** is a polyhedron with 60 golden rhombus faces.

## Construction[edit | edit source]

### Golden rhombohedra[edit | edit source]

The rhombic hexecontahedron can be constructed by joining 20 acute golden rhombohedra around a single point. This gives an easy way to determine the volume of rhombic hexecontahedron given the volume of the acute golden rhombohedron. The volume of a single acute golden rhombohedron of edge length 1 is thus the volume of the rhombic hexecontahedron of edge length 1 is 20 times that making it . The surface area can also be calculated by similar means.

### Stellation[edit | edit source]

The rhombic hexecontahedron is a stellation of the rhombic triacontahedron.

Its stellation is given by the following stellation diagram:

Yellow represents the original face, red represents the new faces, green represents space internal to the new polyhedron and dark blue represents space external to the new polyhedron. Since the faces form coplanar pairs two faces appear in the stellation diagram.

## Related polytopes[edit | edit source]

The rhombic hexecontahedron is topologically equivalent to the deltoidal hexecontahedron which has kites for faces instead of rhombi.

Grünbaum's new rhombic hexecontahedron is another stellation of the rhombic triacontahedron with 60 golden rhombus faces.

## External links[edit | edit source]

- Wikipedia Contributors. "Rhombic hexecontahedron".
- Weisstein, Eric W. "Rhombic Hexecontahedron" at MathWorld.
- McCooey, David. "Rhombic Hexecontahedron"

## References[edit | edit source]

## Bibliography[edit | edit source]

- Grünbaum, Branko (1996a),
*A New Rhombic Hexecontahedron-Once More*(PDF) - Grünbaum, Branko (1996b),
*A New Rhombic Hexecontahedron*(PDF)