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Great Snub Dodecicosidodecahedron

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U64

The great snub dodecicosidodecahedron is the uniform polyhedron with Maeder index 64 (Maeder 1997), Wenninger index 115 (Wenninger 1989), Coxeter index 80 (Coxeter et al. 1954), and Har'El index 69 (Har'El 1993). It has Wythoff symbol |35/35/2 and its faces are 80{3}+24{5/2}.

The great snub dodecicosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[115], UniformPolyhedron["GreatSnubDodecicosidodecahedron"], UniformPolyhedron[{"Coxeter", 80}], UniformPolyhedron[{"Kaleido", 69}], UniformPolyhedron[{"Uniform", 64}], or UniformPolyhedron[{"Wenninger", 115}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatSnubDodecicosidodecahedron"].

Its vertices contain those of the second octahedron 20-compound (E. Weisstein, Aug. 30, 2023).

GreatSnubDodecicosidodecahedralGraph

Its skeleton is the great snub dodecicosidodecahedral graph.

Its circumradius for unit edge length is

R=1/2sqrt(2).

Its dual is the great hexagonal 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. "64: Great Snub Dodecicosidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/64.html.Wenninger, M. J. "Great Snub Dodecicosidodecahedron." Model 115 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 183-185, 1989.

Referenced on Wolfram|Alpha

Great Snub Dodecicosidodecahedron

Cite this as:

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

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