# Inverted snub dodecadodecahedral prism

The **inverted snub dodecadodecahedral prism** or **isdiddip** is a prismatic uniform polychoron that consists of 2 inverted snub dodecadodecahedra, 12 pentagrammic prisms, 12 pentagonal prisms, and 60 triangular prisms. Each vertex joins 1 inverted snub dodecadodecahedron, 1 pentagrammic prism, 1 pentagonal prisms, and 3 triangular prisms. As the name suggests, it is a prism based on the inverted snub dodecadodecahedron.

Inverted snub dodecadodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Isdiddip |

Coxeter diagram | x2s5/3s5s () |

Elements | |

Cells | 60 triangular prisms, 12 pentagonal prisms, 12 pentagrammic prisms, 2 inverted snub dodecadodecahedra |

Faces | 120 triangles, 30+60+60 squares, 24 pentagons, 24 pentagrams |

Edges | 60+60+120+120 |

Vertices | 120 |

Vertex figure | Irregular pentagonal pyramid, edge lengths 1, 1, (1+√5)/2, 1, (√5–1)/2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | ≈ 0.98756 |

Hypervolume | ≈ 4.61431 |

Dichoral angles | Trip–4–trip: ≈ 130.49074° |

Isdid–5/2–stip: 90° | |

Isdid–5–pip: 90° | |

Isdid–3–trip: 90° | |

Trip–4–pip: ≈ 68.64088° | |

Trip–4–stip: ≈ 11.12448° | |

Height | 1 |

Central density | 9 |

Number of pieces | 374 |

Related polytopes | |

Army | Non-uniform Sniddip |

Regiment | Isdiddip |

Dual | Medial inverted pentagonal hexecontahedral tegum |

Conjugate | Snub dodecadodecahedral prism |

Abstract properties | |

Euler characteristic | –8 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{3}+×A_{1}, order 120 |

Convex | No |

Nature | Tame |

Discovered by | {{{discoverer}}} |

## External linksEdit

- Bowers, Jonathan. "Category 19: Prisms" (#956).

- Klitzing, Richard. "isdiddip".