# Great snub icosidodecahedron

Great snub icosidodecahedron
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGosid
Coxeter diagrams5/2s3s ()
Elements
Faces20+60 triangles, 12 pentagrams
Edges30+60+60
Vertices60
Vertex figureIrregular pentagon, edge lengths 1, 1, 1, 1, (5–1)/2
Measures (edge length 1)
Volume≈ 7.67391
Dihedral angles5/2–3: ≈ 138.82237°
3–3: ≈ 126.82315°
Central density7
Number of pieces300
Level of complexity26
Related polytopes
ArmyNon-uniform snub dodecahedron
RegimentGosid
DualGreat pentagonal hexecontahedron
ConjugatesSnub dodecahedron, Great inverted snub icosidodecahedron, great inverted retrosnub icosidodecahedron
Abstract properties
Euler characteristic2
Topological properties
OrientableYes
Properties
SymmetryH3+, order 60
ConvexNo
NatureTame

The great snub icosidodecahedron or gosid is a uniform polyhedron. It consists of 60 snub triangles, 20 additional triangles, and 12 pentagrams. Four triangles and one pentagram meeting at each vertex.

## Measures

The circumradius R ≈ 0.81608 of the great snub icosidodecahedron with unit edge length is the second to largest real root of:

${\displaystyle 4096x^{12}-27648x^{10}+47104x^8-35776x^6+13872x^4-2696x^2+209.}$

Its volume V ≈ 7.67391 is given by the second to largest real root of:

{\displaystyle \begin{align}&2176782336x^{12}-3195335070720x^{10}+162223191936000x^8+1030526618040000x^6\\ {} &+6152923794150000x^4-182124351550575000x^2+187445810737515625.\end{align}}

These same polynomials define the circumradii and volumes of the snub dodecahedron, the great inverted snub icosidodecahedron, and the great inverted retrosnub icosidodecahedron.

## Related polyhedra

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

o3o5/2o truncations
Name OBSA Schläfli symbol CD diagram Picture
Great icosahedron gike {3,5/2} x3o5/2o ()
Truncated great icosahedron tiggy t{3,5/2} x3x5/2o ()
Great icosidodecahedron gid r{3,5/2} o3x5/2o ()
Truncated great stellated dodecahedron (degenerate, ike+2gad) t{5/2,3} o3x5/2x ()
Great stellated dodecahedron gissid {5/2,3} o3o5/2x ()
Small complex rhombicosidodecahedron (degenerate, sidtid+rhom) sicdatrid rr{3,5/2} x3o5/2x ()
Truncated great icosidodecahedron (degenerate, ri+12(10/2)) tr{3,5/2} x3x5/2x ()
Great snub icosidodecahedron gosid sr{3,5/2} s3s5/2s ()