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Great Dodecicosidodecahedron


U61

The great dodecicosidodecahedron is the uniform polyhedron with Maeder index 61 (Maeder 1997), Wenninger index 99 (Wenninger 1989), Coxeter index 77(Coxeter et al. 1954), and Har'El index 66 (Har'El 1993). Its Wythoff symbol is 25/2|3 and its faces are 20{6}+12{5/2},

The great dodecicosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[], UniformPolyhedron["GreatDodecicosidodecahedron"], UniformPolyhedron[{"Coxeter", 77}], UniformPolyhedron[{"Kaleido",66 }], UniformPolyhedron[{"Uniform", 61}], or UniformPolyhedron[{"Wenninger", 114}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatDodecicosidodecahedron"].

SmallRhombicosidodecahedralGraph

Its skeleton is the small rhombicosidodecahedral graph, illustrated above in a few embeddings.

Its circumradius for unit edge length is

 R=1/4sqrt(58-18sqrt(5)).

Its dual is the great dodecacronic 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. "61: Great Dodecicosidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/61.html.Wenninger, M. J. "Great Dodecicosidodecahedron." Modl 99 in Polyhedron Models. Cambridge, England: Cambridge University Press, p. 148, 1989.

Referenced on Wolfram|Alpha

Great Dodecicosidodecahedron

Cite this as:

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

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