# Great quasitruncated icosidodecahedron

Jump to navigation
Jump to search

Great quasitruncated icosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gaquatid |

Coxeter diagram | x5/3x3x () |

Elements | |

Faces | 30 squares, 20 hexagons, 12 decagrams |

Edges | 60+60+60 |

Vertices | 120 |

Vertex figure | Scalene triangle, edge lengths √2, √3, √(5–√5)/2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 10/3–4: |

10/3–6: | |

6–4: | |

Central density | 13 |

Number of external pieces | 1140 |

Level of complexity | 58 |

Related polytopes | |

Army | Semi-uniform Grid, edge lengths (dipentagon-rectangle), (dipentagon-ditrigon), (ditrigon-rectangle) |

Regiment | Gaquatid |

Dual | Great disdyakis triacontahedron |

Conjugate | Great rhombicosidodecahedron |

Convex core | Icosahedron |

Abstract & topological properties | |

Flag count | 720 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **great quasitruncated icosidodecahedron** or **gaquatid**, also called the **great truncated icosidodecahedron**, is a uniform polyhedron. It consists of 12 decagrams, 20 hexagons, and 30 squares, with one of each type of face meeting per vertex. It can be obtained by quasicantitruncation of the great stellated dodecahedron or great icosahedron, or equivalently by quasitruncating the vertices of a great icosidodecahedron and then adjusting the edge lengths to be all equal.

It can be alternated into the great inverted snub icosidodecahedron after equalizing edge lengths.

## Vertex coordinates[edit | edit source]

A great quasitruncated icosidodecahedron of edge length 1 has vertex coordinates given by all permutations of

along with all even permutations of:

## Related polyhedra[edit | edit source]

Name | OBSA | Schläfli symbol | CD diagram | Picture |
---|---|---|---|---|

Great stellated dodecahedron | gissid | {5/3,3} | x5/3o3o () | |

Quasitruncated great stellated dodecahedron | quit gissid | t{5/3,3} | x5/3x3o () | |

Great icosidodecahedron | gid | r{3,5/3} | o5/3x3o () | |

Truncated great icosahedron | tiggy | t{3,5/3} | o5/3x3x () | |

Great icosahedron | gike | {3,5/3} | o5/3o3x () | |

Quasirhombicosidodecahedron | qrid | rr{3,5/3} | x5/3o3x () | |

Great quasitruncated icosidodecahedron | gaquatid | tr{3,5/3} | x5/3x3x () | |

Great inverted snub icosidodecahedron | gisid | sr{3,5/3} | s5/3s3s () |

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 5: Omnitruncates" (#61).

- Klitzing, Richard. "gaquatid".

- Wikipedia Contributors. "Great truncated icosidodecahedron".
- McCooey, David. "Great Truncated Icosidodecahedron"