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Great Stellated Truncated Dodecahedron

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U66

The great stellated truncated dodecahedron, also called the quasitruncated great stellated dodecahedron is the uniform polyhedron with Maeder index 66 (Maeder 1997), Wenninger index 104 (Wenninger 1989), Coxeter index 83 (Coxeter et al. 1954), and Har'El index 71 (Har'El 1993). It has Schläfli symbol t'{5/2,3} and Wythoff symbol 23|5/3. Its faces are 20{3}+12{(10)/3}.

The great stellated truncated dodecahedron is implemented in the Wolfram Language as UniformPolyhedron[104], UniformPolyhedron["GreatStellatedTruncatedDodecahedron"], UniformPolyhedron[{"Coxeter", 83}], UniformPolyhedron[{"Kaleido", 71}], UniformPolyhedron[{"Uniform", 66}], or UniformPolyhedron[{"Wenninger", 104}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatStellatedTruncatedDodecahedron"].

TruncatedDodecahedralGraph

Its skeleton is the truncated dodecahedral graph, illustrated above in a number of embeddings.

Its circumradius for unit edge length is

R=1/4sqrt(74-30sqrt(5)).

Its dual is the great triakis icosahedron.

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. "66: Great Stellated Truncated Dodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/66.html.Wenninger, M. J. "Great Stellated Truncated Dodecahedron." Model 104 in Polyhedron Models. Cambridge, England: Cambridge University Press, p. 161, 1989.

Referenced on Wolfram|Alpha

Great Stellated Truncated Dodecahedron

Cite this as:

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

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