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Truncated Great Dodecahedron

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U37

The truncated great dodecahedron is the uniform polyhedron with Maeder index 37 (Maeder 1997), Wenninger index 75 (Wenninger 1989), Coxeter index 47 (Coxeter et al. 1954), and Har'El index 42 (Har'El 1993). It has Schläfli symbol t{5,5/2} and Wythoff symbol 25/25. Its faces are 12{5/2}+12{10}.

The truncated great dodecahedron is implemented in the Wolfram Language as UniformPolyhedron[75], UniformPolyhedron["TruncatedGreatDodecahedron"], UniformPolyhedron[{"Coxeter", 47}], UniformPolyhedron[{"Kaleido", 42}], UniformPolyhedron[{"Uniform", 37}], or UniformPolyhedron[{"Wenninger", 75}]. It is also implemented in the Wolfram Language as PolyhedronData["TruncatedGreatDodecahedron"].

TruncatedGreatDodecahedralGraph

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

Its circumradius for unit edge lengths

R=1/4sqrt(34+10sqrt(5)).

Its dual polyhedron is the small stellapentakis dodecahedron.

See also

Great Dodecahedron, Truncation, 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. "37: Truncated Great Dodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/37.html.Wenninger, M. J. "Truncated Great Dodecahedron." Model 75 in Polyhedron Models. Cambridge, England: Cambridge University Press, p. 115, 1971.

Referenced on Wolfram|Alpha

Truncated Great Dodecahedron

Cite this as:

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

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