# Great dodecicosidodecahedral prism

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Great dodecicosidodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gaddiddip |

Coxeter diagram | x x5/3x5/2o3*b () |

Elements | |

Cells | 20 triangular prisms, 12 pentagrammic prisms, 12 decagrammic prisms, 2 great dodecicosidodecahedra |

Faces | 40 triangles, 60+60 squares, 24 pentagrams, 24 decagrams |

Edges | 60+120+120 |

Vertices | 120 |

Vertex figure | Isosceles trapezoidal pyramid, edge lengths 1, √(5–√5)/2, (√5–1)/2, √(5–√5)/2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Stip–4–stiddip: |

Trip–4–stiddip: | |

Gaddid–5/2–stip: 90° | |

Gaddid–3–trip: 90° | |

Gaddid–10/3–stiddip: 90° | |

Height | 1 |

Central density | 10 |

Number of pieces | 182 |

Related polytopes | |

Army | Semi-uniform Tipe |

Regiment | Gaddiddip |

Dual | Great dodecacronic hexecontahedral tegum |

Conjugate | Small dodecicosidodecahedral prism |

Abstract properties | |

Euler characteristic | –18 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | No |

Nature | Tame |

The **great dodecicosidodecahedral prism** or **gaddiddip** is a prismatic uniform polychoron that consists of 2 great dodecicosidodecahedra, 12 pentagrammic prisms, 20 triangular prisms, and 12 decagrammic prisms. Each vertex joins 1 great dodecicosidodecahedron, 1 pentagrammic prism, 1 triangular prism, and 2 decagrammic prisms. As the name suggests, it is a prism based on the great dodecicosidodecahedron.

The great dodecicosidodecahedral prism can be vertex-inscribed into the grand ditetrahedronary hexacosidishecatonicosachoron.

## Vertex coordinates[edit | edit source]

The vertices of a great dodecicosidodecahedral 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" (#938).

- Klitzing, Richard. "gaddiddip".