Great snub icosidodecahedron

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Great snub icosidodecahedron
Rank3
TypeUniform
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)
Circumradius≈ 0.81608
Volume≈ 7.67391
Dihedral angles5/2–3: ≈ 138.82237°
 3–3: ≈ 126.82315°
Central density7
Number of external pieces300
Level of complexity26
Related polytopes
ArmyNon-uniform Snid
RegimentGosid
DualGreat pentagonal hexecontahedron
ConjugatesSnub dodecahedron, Great inverted snub icosidodecahedron, great inverted retrosnub icosidodecahedron
Abstract & topological properties
Flag count600
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryH3+, order 60
ChiralYes
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[edit | edit source]

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

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

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[edit | edit source]

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

External links[edit | edit source]