# Disnub icosidodecahedron

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

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Dissid |

Coxeter diagram | |

Elements | |

Components | 2 snub dodecahedra |

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

Edges | 60+120+120 |

Vertices | 120 |

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

Measures (edge length 1) | |

Circumradius | ≈ 2.15584 |

Volume | ≈ 75.23330 |

Dihedral angles | 3–3: ≈ 164.17537° |

5–3: ≈ 152.92992° | |

Central density | 2 |

Number of external pieces | 392 |

Level of complexity | 26 |

Related polytopes | |

Army | Semi-uniform Grid |

Regiment | Dissid |

Dual | Compound of two pentagonal hexecontahedra |

Conjugates | Great disnub icosidodecahedron, great inverted disnub icosidodecahedron, great diretrosnub icosidodecahedron |

Convex core | Icosidodecatruncated disdyakis triacontahedron |

Abstract & topological properties | |

Flag count | 1200 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

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.

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

## 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 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. (2023). "Wolfram|Alpha Knowledgebase". Champaign, IL. "
`PolyhedronData["SnubDodecahedron", {"Circumradius", "Volume", "DihedralAngles"}]`

".