Snub icosidodecadodecahedron

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Snub icosidodecadodecahedron
Snub icosidodecadodecahedron.png
Bowers style acronymSided
Coxeter diagrams5/3s3s5*a (CDel branch hh.pngCDel split2-f5.pngCDel node h.png)
Faces20+60 triangles, 12 pentagons, 12 pentagrams
Vertex figureIrregular hexagon, edge lengths 1, 1, 1, (5–1)/2, 1, (1+5)/2
Snub icosidodecadodecahedron vertfig.png
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
DualMedial hexagonal hexecontahedron
ConjugateSnub icosidodecadodecahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count720
Euler characteristic-16
SymmetryH3+, order 60

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 CDel branch.pngCDel split2-f5.pngCDel node 1.png
Ditrigonal dodecadodecahedron.png
Small complex icosidodecahedron (degenerate, ike+gad) cid CDel branch 01rd.pngCDel split2-f5.pngCDel node.png
Small complex icosidodecahedron.png
Great complex icosidodecahedron (degenerate, sissid+gike) gacid CDel branch 10ru.pngCDel split2-f5.pngCDel node.png
Great complex icosidodecahedron.png
Icosidodecadodecahedron ided CDel branch 11.pngCDel split2-f5.pngCDel node.png
Small ditrigonal dodecicosidodecahedron sidditdid CDel branch 01rd.pngCDel split2-f5.pngCDel node 1.png
Small ditrigonal dodecicosidodecahedron.png
Great ditrigonal dodecicosidodecahedron gidditdid CDel branch 10ru.pngCDel split2-f5.pngCDel node 1.png
Great ditrigonal dodecicosidodecahedron.png
Icosidodecatruncated icosidodecahedron idtid CDel branch 11.pngCDel split2-f5.pngCDel node 1.png
Icositruncated dodecadodecahedron.png
Snub icosidodecadodecahedron sided CDel branch hh.pngCDel split2-f5.pngCDel node h.png
Snub icosidodecadodecahedron.png

External links[edit | edit source]