Snub icosidodecadodecahedron

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Snub icosidodecadodecahedron
Rank3
TypeUniform
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)
Circumradius≈ 1.12690
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
ConjugateSnub icosidodecadodecahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count720
Euler characteristic-16
OrientableYes
Genus9
Properties
SymmetryH3+, order 60
ChiralYes
ConvexNo
NatureTame

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.

Measures[edit | edit source]

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

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

Related polyhedra[edit | edit source]

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
Ditrigonary dodecadodecahedron ditdid
Small complex icosidodecahedron (degenerate, ike+gad) cid
Great complex icosidodecahedron (degenerate, sissid+gike) gacid
Icosidodecadodecahedron ided
Small ditrigonal dodecicosidodecahedron sidditdid
Great ditrigonal dodecicosidodecahedron gidditdid
Icosidodecatruncated icosidodecahedron idtid
Snub icosidodecadodecahedron sided


External links[edit | edit source]