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Great Truncated Icosahedron

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U55

The great truncated icosahedron, also called the truncated great icosahedron, is the uniform polyhedron with Maeder index 55 (Maeder 1997), Wenninger index 95 (Wenninger 1989), Coxeter index 71 (Coxeter et al. 1954), and Har'El index 60 (Har'El 1993). It has Schläfli symbol t{3,5/2} and Wythoff symbol 25/2|3. Its faces are 20{6}+12{5/2}.

The great truncated icosahedron is implemented in the Wolfram Language as UniformPolyhedron[95], UniformPolyhedron["GreatTruncatedIcosahedron"], UniformPolyhedron[{"Coxeter", 71}], UniformPolyhedron[{"Kaleido", 60}], UniformPolyhedron[{"Uniform", 55}], or UniformPolyhedron[{"Wenninger", 95}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatTruncatedIcosahedron"].

Its circumradius for unit edge length is

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

Its dual is the great stellapentakis dodecahedron.

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. "55: Great Truncated Icosahedron." 1997. https://www.mathconsult.ch/static/unipoly/55.html.Wenninger, M. J. "Great Truncated Icosahedron." Model 95 in Polyhedron Models. Cambridge, England: Cambridge University Press, p. 148, 1989.

Referenced on Wolfram|Alpha

Great Truncated Icosahedron

Cite this as:

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

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