# Rhombicosahedron

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Rhombicosahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Ri |

Elements | |

Faces | 30 squares, 20 hexagons |

Edges | 60+60 |

Vertices | 60 |

Vertex figure | Butterfly, edge lengths √2 and √3 |

Measures (edge length 1) | |

Circumradius | |

Dihedral angles | 4–6 #1: |

4–6 #2: | |

Central density | odd |

Number of external pieces | 630 |

Level of complexity | 36 |

Related polytopes | |

Army | Semi-uniform ti, edge lengths (pentagons), (between ditrigons) |

Regiment | Raded |

Dual | Rhombicosacron |

Conjugate | Rhombicosahedron |

Convex core | Icosahedron |

Abstract & topological properties | |

Flag count | 480 |

Euler characteristic | –10 |

Orientable | No |

Genus | 12 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **rhombicosahedron**, or **ri**, is a uniform polyhedron. It consists of 30 squares and 20 hexagons. Two squares and two hexagons meet at each vertex.

It is a faceting of the rhombidodecadodecahedron, using its 30 squares along with the 20 hexagons of the icosidodecadodecahedron.

The truncated great icosidodecahedron (x5/2x3x) is a degenerate polyhedron with 20 hexagons, 30 squares, and 12 doubly-wound pentagons. If those pentagrams are blended out, the result is the rhombicosahedron.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the rhombidodecadodecahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#44).

- Klitzing, Richard. "ri".

- Wikipedia Contributors. "Rhombicosahedron".
- McCooey, David. "Rhombicosahedron"