# Disnub icosidodecadodecahedron

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Disnub icosidodecadodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Desided |

Elements | |

Components | 2 snub icosidodecadodecahedra |

Faces | 120 triangles, 40 triangles as 20 hexagrams, 24 pentagons as 12 stellated decagons, 24 pentagrams as 12 stellated decagrams |

Edges | 120+120+120 |

Vertices | 120 |

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

Measures (edge length 1) | |

Circumradius | ≈ 1.12690 |

Volume | ≈ 29.28396 |

Dihedral angles | 3–3: ≈ 146.78125° |

5–3: ≈ 120.43401° | |

5/2–3: ≈ 7.35214° | |

Central density | 8 |

Number of external pieces | 752 |

Level of complexity | 47 |

Related polytopes | |

Army | Semi-uniform Grid |

Regiment | Desided |

Dual | Compound of two medial hexagonal hexecontahedra |

Conjugate | Disnub icosidodecadodecahedron |

Convex core | Dodecahedron |

Abstract & topological properties | |

Flag count | 1440 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **disnub icosidodecadodecahedron**, **desided**, or **compound of two snub icosidodecadodecahedra** is a uniform polyhedron compound. It consists of 120 snub triangles, 40 further triangles, 24 pentagons, and 24 pentagrams (the latter three can combine in pairs due to faces in the same plane). Four triangles, one pentagon, and one pentagram join at each vertex.

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

## Measures[edit | edit source]

The circumradius of the disnub icosidodecadodecahedron with unit edge length is the greatest real root of

Its volume is given by the positive real root of

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C10: Disnubs" (#74).

- Klitzing, Richard. "desided".

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