# Snub dodecadodecahedron

Snub dodecadodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Siddid |

Coxeter diagram | s5/2s5s () |

Elements | |

Faces | 60 triangles, 12 pentagons, 12 pentagrams |

Edges | 30+60+60 |

Vertices | 60 |

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

Measures (edge length 1) | |

Circumradius | ≈ 1.27444 |

Volume | ≈ 18.25642 |

Dihedral angles | 5/2–3: ≈ 157.77792° |

3–3: ≈ 151.48799° | |

5–3: ≈ 129.79515° | |

Central density | 3 |

Number of external pieces | 432 |

Level of complexity | 29 |

Related polytopes | |

Army | Non-uniform Snid |

Regiment | Siddid |

Dual | Medial pentagonal hexecontahedron |

Conjugate | Inverted snub dodecadodecahedron |

Abstract & topological properties | |

Flag count | 600 |

Euler characteristic | -6 |

Orientable | Yes |

Genus | 4 |

Properties | |

Symmetry | H_{3}+, order 60 |

Convex | No |

Nature | Tame |

The **snub dodecadodecahedron** or **siddid**, is a uniform polyhedron. It consists of 60 snub triangles, 12 pentagrams, and 12 pentagons. Three triangles, 1 pentagon, and one pentagram meeting at each vertex.

## Measures

The circumradius *R* ≈ 1.27444 of the snub dodecadodecahedron with unit edge length is the largest real root of:

Its volume *V* ≈ 18.25642 is given by the largest real root of:

These same polynomials define the circumradius and volume of the inverted snub dodecadodecahedron.

## Related polyhedra

The disnub dodecadodecahedron is a uniform polyhedron compound composed of the 2 opposite chiral forms of the snub dodecadodecahedron.

## External links

- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#66).

- Klitzing, Richard. "siddid".
- Wikipedia contributors. "Snub dodecadodecahedron".
- McCooey, David. "Snub Dodecadodecahedron"