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Great Inverted Snub Icosidodecahedron

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U69

The great inverted snub icosidodecahedron is the uniform polyhedron with Maeder index 69 (Maeder 1997), Wenninger index 113 (Wenninger 1989), Coxeter index 73 (Coxeter et al. 1954), and Har'El index 74 (Har'El 1993). It has Wythoff symbol |235/2 and its faces are 80{3}+12{5/2}.

The great inverted snub icosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[113], UniformPolyhedron["GreatInvertedSnubIcosidodecahedron"], UniformPolyhedron[{"Coxeter", 73}], UniformPolyhedron[{"Kaleido", 74}], UniformPolyhedron[{"Uniform", 69}], or UniformPolyhedron[{"Wenninger", 113}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatInvertedSnubIcosidodecahedron"].

SnubDodecahedralGraph

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

For unit edge length, it has circumradius

R=(209-2696x^2+13872x^4-35776x^6+47104x^8-27648x^(10)+4096x^(12))_6
(1)
approx 0.645020237...,
(2)

where (p(x))_n is the nth root of the polynomial p(x).

Its dual is the great inverted pentagonal hexecontahedron.

See also

Snub Dodecahedron, 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. "69: Great Inverted Snub Icosidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/69.html.Wenninger, M. J. "Great Inverted Snub Icosidodecahedron." Model 113 Polyhedron Models. Cambridge, England: Cambridge University Press, p. 179, 1989.

Cite this as:

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

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