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Small Snub Icosicosidodecahedron

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U32

The small snub icosicosidodecahedron is the uniform polyhedron with Maeder index 32 (Maeder 1997), Wenninger index 110 (Wenninger 1989), Coxeter index 41 (Coxeter et al. 1954), and Har'El index 37 (Har'El 1993). It has Wythoff symbol |335/2 and faces 100{3}+12{5/2}.

The small snub icosicosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[110], UniformPolyhedron["SmallSnubIcosicosidodecahedron"], UniformPolyhedron[{"Coxeter", 41}], UniformPolyhedron[{"Kaleido", 37}], UniformPolyhedron[{"Uniform", 32}], or UniformPolyhedron[{"Wenninger", 110}]. It is also implemented in the Wolfram Language as PolyhedronData["SmallSnubIcosicosidodecahedron"].

SmallSnubIcosicosidodecahedralGraph

Its skeleton is the small snub icosicosidodecahedral graph, illustrated above in a number of embeddings.

Its circumradius for unit edge lengths is

R=1/4sqrt(13+3sqrt(5)+sqrt(102+46sqrt(5)))
(1)
=1.4581903307387....
(2)

Its dual polyhedron is the small hexagonal hexecontahedron.

See also

Small Hexagonal Hexecontahedron, Uniform Polyhedron

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References

Coxeter, H. S. M.; Longuet-Higgins, M. S.; and Miller, J. C. P. "Uniform Polyhedra." Phil. Trans. Roy. Soc. London Ser. A 246, 401-450, 1954.Har'El, Z. "Uniform Solution for Uniform Polyhedra." Geometriae Dedicata 47, 57-110, 1993.Maeder, R. E. "32: Small Snub Icosicosidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/32.html.Wenninger, M. J. "Small Snub Icosicosidodecahedron." Model 110 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 172-173, 1971.

Referenced on Wolfram|Alpha

Small Snub Icosicosidodecahedron

Cite this as:

Weisstein, Eric W. "Small Snub Icosicosidodecahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SmallSnubIcosicosidodecahedron.html

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