# Disnub dodecadodecahedron

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Disnub dodecadodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Disdid |

Elements | |

Components | 2 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 | ≈ 1.27444 |

Volume | ≈ 36.51284 |

Dihedral angles | 5–3: ≈ 157.77792° |

3–3: ≈ 151.48799° | |

5/2–3: ≈ 129.79515° | |

Central density | 6 |

Number of external pieces | 1092 |

Level of complexity | 64 |

Related polytopes | |

Army | Semi-uniform Grid |

Regiment | Disdid |

Dual | Compound of two medial pentagonal hexecontahedra |

Conjugate | Inverted disnub dodecadodecahedron |

Abstract & topological properties | |

Flag count | 1200 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **disnub dodecadodecahedron**, **disdid**, or **compound of two 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.

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

## Measures[edit | edit source]

The circumradius of the disnub dodecadodecahedron with unit edge length is the largest real root of:

Its volume is given by the largest real root of:

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C10: Disnubs" (#70).

- Klitzing, Richard. "disdid".

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