# Great dirhombicosidodecahedron

Great dirhombicosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Gidrid |

Coxeter diagram | s3s5/2s3/2s5/3*aØ*c *bØ*d |

Elements | |

Faces | 40 triangles, 60 squares, 24 pentagrams |

Edges | 120+120 |

Vertices | 60 |

Vertex figure | Irregular octagon, edge lengths 1, √2, (√5–1)/2, √2, 1, √2, (√5–1)/2, √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | 0 |

Dihedral angles | 5/2–4: |

3–4: | |

Central density | 0 |

Number of external pieces | 3000 |

Level of complexity | 164 |

Related polytopes | |

Army | Semi-uniform srid, edge lengths (pentagons), (triangles) |

Regiment | Gidrid |

Dual | Great dirhombicosidodecacron |

Conjugate | Great dirhombicosidodecahedron |

Abstract & topological properties | |

Flag count | 960 |

Euler characteristic | –56 |

Orientable | Yes |

Genus | 29 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 8 |

Convex | No |

Nature | Tame |

The **great dirhombicosidodecahedron**, **Miller's monster**, or **gidrid**, is a uniform star polyhedron. It is the most complex of the ten uniform hemipolyhedra. It consists of 40 triangles, 60 snub squares, and 24 pentagrams, all of which fall into coinciding planes in pairs. Two triangles, four squares, and two pentagrams meet at each vertex.

## Vertex coordinates[edit | edit source]

A great dirhombicosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:

- ,
- ,
- .

## Related polyhedra[edit | edit source]

The great dirhombicosidodecahedron has the same edges as two uniform polyhedron compounds: the disnub icosahedron, the compound of 20 octahedra, and the snub pseudosnub rhombicosahedron, the compound of 20 tetrahemihexahedra. It also has the same vertices of the great snub dodecicosidodecahedron, which uses a subset of its edges.

The degenerate great disnub dirhombidodecahedron can be constructed by blending this polyhedron with the disnub icosahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#75).

- Klitzing, Richard. "gidrid".
- Wikipedia contributors. "Great dirhombicosidodecahedron".
- McCooey, David. "Great Dirhombicosidodecahedron"