Snub dodecadodecahedron

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Snub dodecadodecahedron
Snub dodecadodecahedron.png
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSiddid
Coxeter diagrams5/2s5s (CDel node h.pngCDel 5-2.pngCDel node h.pngCDel 5.pngCDel node h.png)
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
Snub dodecadodecahedron vertfig.png
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 pieces432
Level of complexity29
Related polytopes
ArmyNon-uniform snub dodecahedron
RegimentSiddid
DualMedial pentagonal hexecontahedron
ConjugateInverted snub dodecadodecahedron
Abstract properties
Euler characteristic-6
Topological properties
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[edit | edit source]

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[edit | edit source]

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

o5o5/2o truncations
Name OBSA Schläfli symbol CD diagram Picture
Great dodecahedron gad {5,5/2} x5o5/2o (CDel node 1.pngCDel 5.pngCDel node.pngCDel 5-2.pngCDel node.png)
Great dodecahedron.png
Truncated great dodecahedron tigid t{5,5/2} x5x5/2o (CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 5-2.pngCDel node.png)
Great truncated dodecahedron.png
Dodecadodecahedron did r{5,5/2} o5x5/2o (CDel node.pngCDel 5.pngCDel node 1.pngCDel 5-2.pngCDel node.png)
Dodecadodecahedron.png
Truncated small stellated dodecahedron (degenerate, triple cover of doe) t{5/2,5} o5x5/2x (CDel node.pngCDel 5.pngCDel node 1.pngCDel 5-2.pngCDel node 1.png)
Dodecahedron.png
Small stellated dodecahedron sissid {5/2,5} o5o5/2x (CDel node.pngCDel 5.pngCDel node.pngCDel 5-2.pngCDel node 1.png)
Small stellated dodecahedron.png
Rhombidodecadodecahedron raded rr{5,5/2} x5o5/2x (CDel node 1.pngCDel 5.pngCDel node.pngCDel 5-2.pngCDel node 1.png)
Rhombidodecadodecahedron.png
Truncated dodecadodecahedron (degenerate, sird+12(10/2)) tr{5,5/2} x5x5/2x (CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 5-2.pngCDel node 1.png)
Snub dodecadodecahedron siddid sr{5,5/2} s5s5/2s (CDel node h.pngCDel 5.pngCDel node h.pngCDel 5-2.pngCDel node h.png)
Snub dodecadodecahedron.png

External links[edit | edit source]