# Rhombidodecadodecahedron

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Rhombidodecadodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Raded |

Coxeter diagram | x5/2o5x () |

Elements | |

Faces | 30 squares, 12 pentagons, 12 pentagrams |

Edges | 60+60 |

Vertices | 60 |

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–5/2: |

4–5: | |

Central density | 3 |

Number of external pieces | 288 |

Level of complexity | 19 |

Related polytopes | |

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

Regiment | Raded |

Dual | Medial deltoidal hexecontahedron |

Conjugate | Rhombidodecadodecahedron |

Convex core | Chamfered dodecahedron |

Abstract & topological properties | |

Flag count | 480 |

Euler characteristic | -6 |

Orientable | Yes |

Genus | 4 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **rhombidodecadodecahedron**, or **raded**, is a uniform polyhedron. It consists of 30 squares, 12 pentagons, and 12 pentagrams. One pentagon, one pentagram, and two squares join at each vertex. It can be obtained by cantellation of the small stellated dodecahedron or great dodecahedron, or equivalently by expanding either polyhedron's faces outward and filling in the gaps with appropriate faces.

## Vertex coordinates[edit | edit source]

A rhombidodecadodecahedron of edge length 1 has vertex coordinates given by all permutations of

along with all even permutations of

## Related polyhedra[edit | edit source]

The rhombidodecadodecahedron is the colonel of a three-member regiment that also includes the icosidodecadodecahedron and the rhombicosahedron.

Oddly, it has the same circumradius as the cuboctatruncated cuboctahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#42).

- Klitzing, Richard. "raded".
- Wikipedia contributors. "Rhombidodecadodecahedron".
- McCooey, David. "Rhombidodecadodecahedron"