# Great quasitruncated icosidodecahedral prism

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Great quasitruncated icosidodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Gaquatiddip |

Coxeter diagram | x x5/3x3x () |

Elements | |

Cells | 30 cubes, 20 hexagonal prisms, 12 decagrammic prisms, 2 great quasitruncated icosidodecahedra |

Faces | 60+60+60+60 squares, 40 hexagons, 24 decagrams |

Edges | 120+120+120+120 |

Vertices | 240 |

Vertex figure | Irregular tetrahedron, edge lengths √2, √3, √(5–√5)/2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Cube–4–stiddip: |

Gaquatid–10/3–stiddip: 90° | |

Gaquatid–6–hip: 90° | |

Gaquatid–4–cube: 90° | |

Hip–4–stiddip: | |

Cube–4–hip: | |

Height | 1 |

Central density | 13 |

Number of external pieces | 1142 |

Related polytopes | |

Army | Semi-uniform Griddip |

Regiment | Gaquatiddip |

Dual | Great disdyakis triacontahedral tegum |

Conjugate | Great rhombicosidodecahedral prism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | No |

Nature | Tame |

The **great quasitruncated icosidodecahedral prism** or **gaquatiddip**, is a prismatic uniform polychoron that consists of 2 great quasitruncated icosidodecahedra, 12 decagrammic prisms, 20 hexagonal prisms, and 30 cubes. Each vertex joins one of each type of cell. as the name suggests, it is a prism based on the great quasitruncated icosidodecahedron.

The great rhombicosidodecahedral pirsm can be vertex-inscribed into the great tritrigonary hexacositrishecatonicosachoron.

## Vertex coordinates[edit | edit source]

The vertices of a great quasitruncated icosidodecahedral prism of edge length 1 are given by all permutations of the first three coordinates of:

along with all even permutations of the first three coordinates of:

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#948).

- Klitzing, Richard. "gaquatiddip".