# Quasitruncated great stellated dodecahedron

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Quasitruncated great stellated dodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Quit gissid |

Coxeter diagram | x5/3x3o () |

Elements | |

Faces | 20 triangles, 12 decagrams |

Edges | 30+60 |

Vertices | 60 |

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 10/3–3: |

10/3–10/3: | |

Central density | 13 |

Number of external pieces | 120 |

Level of complexity | 9 |

Related polytopes | |

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

Regiment | Quit gissid |

Dual | Great triakis icosahedron |

Conjugate | Truncated dodecahedron |

Convex core | Dodecahedron |

Abstract & topological properties | |

Flag count | 360 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **quasitruncated great stellated dodecahedron**, or **quit gissid**, also called the **great stellated truncated dodecahedron**, is a uniform polyhedron. It consists of 20 triangles and 12 decagrams. Each vertex joins one triangle and two decagrams. As the name suggests, it can be obtained by quasitruncation of the great stellated dodecahedron.

## Vertex coordinates[edit | edit source]

A quasitruncated great stellated dodecahedron of edge length 1 has vertex coordinates given by 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 2: Truncates" (#19).

- Klitzing, Richard. "Quit gissid".

- Wikipedia Contributors. "Great stellated truncated dodecahedron".
- McCooey, David. "Great Stellated Truncated Dodecahedron"