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.

Rank3
TypeUniform
Notation
Bowers style acronymSiddid
Coxeter diagrams5/2s5s ()
Elements
Faces60 triangles, 12 pentagons, 12 pentagrams
Edges30+60+60
Vertices60
Vertex figureIrregular pentagon, edge lengths 1, 1, (5–1)/2, 1, (1+5)/2
Measures (edge length 1)
Volume≈ 18.25642
Dihedral angles5/2–3: ≈ 157.77792°
3–3: ≈ 151.48799°
5–3: ≈ 129.79515°
Central density3
Number of external pieces432
Level of complexity29
Related polytopes
ArmyNon-uniform Snid
RegimentSiddid
DualMedial pentagonal hexecontahedron
Abstract & topological properties
Flag count600
Euler characteristic-6
OrientableYes
Genus4
Properties
SymmetryH3+, order 60
ChiralYes
ConvexNo
NatureTame

## Measures

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

${\displaystyle 64x^{8}-192x^{6}+180x^{4}-65x^{2}+8.}$

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

${\displaystyle 64x^{8}-21440x^{6}+18100x^{4}+5895625x^{2}+60062500.}$

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.