# Great snub icosidodecahedron

(Redirected from Gosid)

Great snub icosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Gosid |

Coxeter diagram | s5/2s3s () |

Elements | |

Faces | 20+60 triangles, 12 pentagrams |

Edges | 30+60+60 |

Vertices | 60 |

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

Measures (edge length 1) | |

Circumradius | ≈ 0.81608 |

Volume | ≈ 7.67391 |

Dihedral angles | 5/2–3: ≈ 138.82237° |

3–3: ≈ 126.82315° | |

Central density | 7 |

Number of external pieces | 300 |

Level of complexity | 26 |

Related polytopes | |

Army | Non-uniform Snid |

Regiment | Gosid |

Dual | Great pentagonal hexecontahedron |

Conjugates | Snub dodecahedron, Great inverted snub icosidodecahedron, great inverted retrosnub icosidodecahedron |

Abstract & topological properties | |

Flag count | 600 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{3}+, order 60 |

Chiral | Yes |

Convex | No |

Nature | Tame |

The **great snub icosidodecahedron** or **gosid** is a uniform polyhedron. It consists of 60 snub triangles, 20 additional triangles, and 12 pentagrams. Four triangles and one pentagram meeting at each vertex.

## Measures[edit | edit source]

The circumradius *R* ≈ 0.81608 of the great snub icosidodecahedron with unit edge length is the second to largest real root of:

Its volume *V* ≈ 7.67391 is given by the second to largest real root of:

These same polynomials define the circumradii and volumes of the snub dodecahedron, the great inverted snub icosidodecahedron, and the great inverted retrosnub icosidodecahedron.

## Related polyhedra[edit | edit source]

The great disnub icosidodecahedron is a uniform polyhedron compound composed of the 2 opposite chiral forms of the great snub icosidodecahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#67).

- Klitzing, Richard. "gosid".
- Wikipedia contributors. "Great snub icosidodecahedron".
- McCooey, David. "Great Snub Icosidodecahedron"