# Disnub icosidodecahedron

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Disnub icosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Dissid |

Info | |

Symmetry | H3, order 120 |

Army | Semi-uniform Grid |

Regiment | Dissid |

Elements | |

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

Components | 2 snub dodecahedra |

Faces | 120 triangles, 20 hexagrams, 12 stellated decagons |

Edges | 60+120+120 |

Vertices | 120 |

Measures (edge length 1) | |

Circumradius | ≈ 2.15584 |

Volume | ≈ 75.23330 |

Dihedral angles | 3–3: ≈ 164.17537° |

5–3: ≈ 152.92992° | |

Central density | 2 |

Related polytopes | |

Dual | Compound of two pentagonal hexecontahedra |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

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

## Measures[edit | edit source]

The circumradius *R* ≈ 2.15584 of the disnub icosidodecahedron with unit edge length is the largest real root of

Its volume *V* ≈ 75.23330 is given by twice the largest real root of

Its dihedral angles may be given as acos(*α*) for the angle between two triangles, and acos(*β*) for the angle between a pentagon and a triangle, where *α* ≈ –0.96210 is the smallest real root of

and *β* ≈ –0.89045 is the second to smallest root of

^{[1]}

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C10: Disnubs" (#69).

- Klitzing, Richard. "Dissid".

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

- ↑ Wolfram Research, Inc. (2021). "Wolfram|Alpha Knowledgebase". Champaign, IL. "
`PolyhedronData["SnubDodecahedron", {"Circumradius", "Volume", "DihedralAngles"}]`

".