# Inverted disnub dodecadodecahedron

The **inverted disnub dodecadodecahedron**, **idisdid**, or **compound of two inverted snub dodecadodecahedra** is a uniform polyhedron compound. It consists of 120 snub triangles, 24 pentagons, and 24 pentagrams (the latter two can combine in pairs due to faces in the same plane). Three triangles, one pentagon, and one pentagram join at each vertex.

Inverted disnub dodecadodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Idisdid |

Elements | |

Components | 2 inverted snub dodecadodecahedra |

Faces | 120 triangles, 24 pentagons as 12 stellated decagons, 24 pentagrams as 12 stellated decagrams |

Edges | 60+120+120 |

Vertices | 120 |

Vertex figure | Irregular pentagon, edge lengths 1, 1, (√5–1)/2, 1, (1+√5)/2 |

Measures (edge length 1) | |

Circumradius | ≈ 0.85163 |

Volume | ≈ 9.22862 |

Dihedral angles | 3–3: ≈ 130.49074° |

5–3: ≈ 68.64088 | |

5/2–3: ≈ 11.12448° | |

Central density | 18 |

Number of external pieces | 1752 |

Level of complexity | 112 |

Related polytopes | |

Army | Semi-uniform Grid |

Regiment | Idisdid |

Dual | Compound of two medial inverted pentagonal hexecontahedra |

Conjugate | Disnub dodecadodecahedron |

Convex core | Dodecahedron |

Abstract & topological properties | |

Flag count | 1200 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

Its quotient prismatic equivalent is the inverted snub dodecadodecahedral antiprism, which is four-dimensional.

## MeasuresEdit

The circumradius of the inverted disnub dodecadodecahedron with unit edge length is the smallest positive real root of:

Its volume is given by the smallest positive real root of:

## External linksEdit

- Bowers, Jonathan. "Polyhedron Category C10: Disnubs" (#72).

- Klitzing, Richard. "idisdid".

- Wikipedia Contributors. "Compound of two inverted snub dodecadodecahedra".