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Truncated Dodecadodecahedron


U59

The truncated dodecadodecahedron, also called the quasitruncated dodecahedron, is the uniform polyhedron with Maeder index 59 (Maeder 1997), Wenninger index 98 (Wenninger 1989), Coxeter index 75 (Coxeter et al. 1954), and Har'El index 65 (Har'El 1993). It has Schläfli symbol t'{5/2; 5} and Wythoff symbol 25/3|5. Its faces are 12{10}+30{4}+12{(10)/3}.

The truncated dodecadodecahedron is implemented in the Wolfram Language as UniformPolyhedron[98], UniformPolyhedron["TruncatedDodecadodecahedron"], UniformPolyhedron[{"Coxeter",75 }], UniformPolyhedron[{"Kaleido", 65}], UniformPolyhedron[{"Uniform",59 }], or UniformPolyhedron[{"Wenninger", 98}]. It is also implemented in the Wolfram Language as PolyhedronData["TruncatedDodecadodecahedron"].

TruncatedDodecadodecahedralGraph

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

Its circumradius for unit edge lengths

 R=1/2sqrt(11).

Its dual polyhedron is the medial disdyakis triacontahedron.


See also

Medial Disdyakis Triacontahedron, 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. "59: Truncated Dodecadodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/59.html.Wenninger, M. J. "Truncated Dodecadodecahedron." Model 98 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 152-153, 1989.

Referenced on Wolfram|Alpha

Truncated Dodecadodecahedron

Cite this as:

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

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