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Great Truncated Icosidodecahedron

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U68

The great truncated icosidodecahedron, also called the great quasitruncated icosidodecahedron, is the uniform polyhedron with Maeder index 68 (Maeder 1997), Wenninger index 108 (Wenninger 1989), Coxeter index 87 (Coxeter et al. 1954), and Har'El index 73 (Har'El 1993). It has Schläfli symbol t^'{3; 5/2} and Wythoff symbol 235/3|. Its faces are 20{6}+30{4}+12{(10)/3}.

The great truncated icosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[108], UniformPolyhedron["GreatTruncatedIcosidodecahedron"], UniformPolyhedron[{"Coxeter", 87}], UniformPolyhedron[{"Kaleido", 73}], UniformPolyhedron[{"Uniform", 68}], or UniformPolyhedron[{"Wenninger", 108}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatTruncatedIcosidodecahedron"].

GreatRhombicosidodecahedralGraph

Its skeleton graph is the great rhombicosidodecahedral graph, illustrated above.

Its circumradius for unit edge length is

R=1/2sqrt(31-12sqrt(5)).

Its dual is the great disdyakis triacontahedron.

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. "68: Great Truncated Icosidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/68.html.Wenninger, M. J. "Great Truncated Icosidodecahedron." Model 108 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 166-167, 1989.

Referenced on Wolfram|Alpha

Great Truncated Icosidodecahedron

Cite this as:

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

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