# Icosidodecadodecahedral prism

The **icosidodecadodecahedral prism** or **ididdip** is a prismatic uniform polychoron that consists of 2 icosidodecadodecahedra, 12 pentagonal prisms, 12 pentagrammic prisms, and 20 hexagonal prisms. Each vertex joins 1 icosidodecadodecahedron, 1 pentagonal prism, 1 pentagrammic prism, and 2 hexagonal prisms. As the name suggests, it is a prism based on the icosidodecadodecahedron.

Icosidodecadodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Ididdip |

Coxeter diagram | x o5/3x3x5*b () |

Elements | |

Cells | 12 pentagonal prisms, 12 pentagrammic prisms, 20 hexagonal prisms, 2 icosidodecadodecahedra |

Faces | 60+60 squares, 24 pentagons, 24 pentagrams, 40 hexagons |

Edges | 60+120+120 |

Vertices | 120 |

Vertex figure | Crossed isosceles trapezoidal pyramid, edge lengths (√5–1)/2, √3, (1+√5)/2, √3 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | 20 |

Dichoral angles | Pip–4–hip: |

Ided–5/2–stip: 90° | |

Ided–5–pip: 90° | |

Ided–6–hip: 90° | |

Stip–4–hip: | |

Height | 1 |

Central density | 4 |

Number of external pieces | 434 |

Related polytopes | |

Army | Semi-uniform Tipe |

Regiment | Radiddip |

Dual | Medial icosacronic hexecontahedral tegum |

Conjugate | Icosidodecadodecahedral prism |

Abstract & topological properties | |

Euler characteristic | –18 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | No |

Nature | Tame |

## Vertex coordinatesEdit

Its vertices are the same as those of its regiment colonel, the rhombidodecadodecahedral prism.

## External linksEdit

- Bowers, Jonathan. "Category 19: Prisms" (#930).

- Klitzing, Richard. "ididdip".