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Great Retrosnub Icosidodecahedron

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U74

The great retrosnub icosidodecahedron, also called the great inverted retrosnub icosidodecahedron is the uniform polyhedron with Maeder index 74 (Maeder 1997), Wenninger index 117 (Wenninger 1989), Coxeter index 90 (Coxeter et al. 1954), and Har'El index 79 (Har'El 1993). It has Wythoff symbol |23/25/3 and its faces are 80{3}+12{5/2}.

The great retrosnub icosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[117], UniformPolyhedron["GreatRetrosnubIcosidodecahedron"], UniformPolyhedron[{"Coxeter", 90}], UniformPolyhedron[{"Kaleido", 79}], UniformPolyhedron[{"Uniform", 74}], or UniformPolyhedron[{"Wenninger", 117}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatRetrosnubIcosidodecahedron"].

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-y)/(1-y))
(1)
=(4096x^(12)-27648x^(10)+47104x^8-35776x^6+13872x^4-2696x^2+209)_5
(2)
approx 0.5800015,
(3)

where y approx -1.89346 is the smaller negative root of

y^3+2y^2-phi^(-2)=0,
(4)

and phi is the golden ratio.

Its dual is the great pentagrammic 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. "74: Great Retrosnub Icosidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/74.html.Wenninger, M. J. "Great Retrosnub Icosidodecahedron." Model 117 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 189-193, 1989.

Referenced on Wolfram|Alpha

Great Retrosnub Icosidodecahedron

Cite this as:

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

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