# Great disnub dirhombidodecahedron

The **great disnub dirhombidodecahedron**, or **gidisdrid**, also known as Skilling's figure, is a exotic uniform polyhedroid. It consists of 120 snub triangles, 60 snub squares, and 24 pentagrams, the latter two of which fall into coinciding planes in pairs. Six triangles, four squares, and two pentagrams meet at each vertex.

Great disnub dirhombidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gidisdrid |

Elements | |

Faces | 120 triangles, 60 squares, 24 pentagrams |

Edges | 120+120+120 |

Vertices | 60 |

Vertex figure | Mirror-symmetric dodecagon, edge lengths (√5–1)/2, √2, 1, 1, 1, √2, (√5–1)/2, √2, 1, 1, 1, √2 |

Measures (edge length 1) | |

Circumradius | |

Dihedral angles | 3–3: |

5/2–4: | |

3–4: | |

Related polytopes | |

Army | Semi-uniform Srid |

Regiment | Gidrid |

Dual | Great disnub dirhombidodecacron |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

As a polyhedron, it is usually considered degenerate because some of the edges coincide in pairs, leading to some edges where four faces can appear to connect. It is the only exotic uniform polyhedroid not analyzable as a compound, and the most well-known example of an exotic polytopoid. J. Skilling announced the discovery of the great disnub dirhombidodecahedron in a 1975 paper, in which computer search was used to prove the list of uniform polyhedra complete.^{[1]}

It can be constructed as a blend of the uniform great dirhombicosidodecahedron and the disnub icosahedron, the uniform compound of 20 octahedra with which it shares its edge skeleton.

## ReferencesEdit

- ↑ Skilling, J. "The Complete Set of Uniform Polyhedra."

## External linksEdit

- Klitzing, Richard. "gidisdrid".

- Wikipedia Contributors. "Great disnub dirhombidodecahedron".