The snub icosidodecadodecahedron or sided, is a uniform polyhedron. It consists of 60 snub triangles, 20 additional triangles, 12 pentagrams, and 12 pentagons. Four triangles, one pentagon, and one pentagram meeting at each vertex. It can be constructed by alternation of the icosidodecatruncated icosidodecahedron and then setting all edge lengths to be equal.

Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSided
Coxeter diagrams5/3s3s5*a ()
Elements
Faces20+60 triangles, 12 pentagons, 12 pentagrams
Edges60+60+60
Vertices60
Vertex figureIrregular hexagon, edge lengths 1, 1, 1, (5–1)/2, 1, (1+5)/2
Measures (edge length 1)
Volume≈ 14.64198
Dihedral angles3–3: ≈ 146.78125°
5–3: ≈ 120.43401°
5/2–3: ≈ 7.35214°
Central density4
Number of external pieces452
Level of complexity31
Related polytopes
ArmyNon-uniform Snid
RegimentSided
DualMedial hexagonal hexecontahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count720
Euler characteristic-16
OrientableYes
Genus9
Properties
SymmetryH3+, order 60
ConvexNo
NatureTame

## Measures

The circumradius R ≈ 1.12690 of the snub icosidodecadodecahedron with unit edge length is the greatest real root of

${\displaystyle 64x^6-128x^4+68x^2-11.}$

Its volume V ≈ 14.64198 is given by the positive real root of

${\displaystyle 729x^6-155520x^4-10125x^2-33153125.}$

## Related polyhedra

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

o5/3o3o5*a truncations
Name OBSA CD diagram Picture