Snub dodecadodecahedron

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Snub dodecadodecahedron
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)
Circumradius≈ 1.27444
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
ConjugateInverted snub dodecadodecahedron
Abstract & topological properties
Flag count600
Euler characteristic-6
OrientableYes
Genus4
Properties
SymmetryH3+, order 60
ConvexNo
NatureTame

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.

Measures

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

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

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.

External links