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Great Snub Icosidodecahedron

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U57

The great snub icosidodecahedron is the uniform polyhedron with Maeder index 57 (Maeder 1997), Wenninger index 116 (Wenninger 1989), Coxeter index 88 (Coxeter et al. 1954), and Har'El index 62 (Har'El 1993). It has Wythoff symbol |235/3 and faces are 80{3}+12{5/2}.

The great snub icosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[116], UniformPolyhedron["GreatSnubIcosidodecahedron"], UniformPolyhedron[{"Coxeter", 88}], UniformPolyhedron[{"Kaleido", 62}], UniformPolyhedron[{"Uniform", 57}], or UniformPolyhedron[{"Wenninger", 116}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatSnubIcosidodecahedron"].

SnubDodecahedralGraph

Its skeleton is the snub dodecahedral graph, illustrated above in a few embeddings.

For unit edge length, it has circumradius

R=1/2sqrt((2-x)/(1-x)) approx 0.6450202,

where x is the most negative root of

x^3+2x^2-phi^(-2)=0,

with phi the golden ratio.

Its dual is the great pentagonal hexecontahedron.

See also

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. "57: Great Snub Icosidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/57.html.Wenninger, M. J. "Great Snub Icosidodecahedron." Model 116 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 186-188, 1989.

Referenced on Wolfram|Alpha

Great Snub Icosidodecahedron

Cite this as:

Weisstein, Eric W. "Great Snub Icosidodecahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GreatSnubIcosidodecahedron.html

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