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Rhombidodecadodecahedron


U38

par The rhombidodecadodecahedron is the uniform polyhedron with Maeder index 38 (Maeder 1997), Wenninger index 76 (Wenninger 1989), Coxeter index 48 (Coxeter et al. 1954), and Har'El index 42 (Har'El 1993). It has Schläfli symbol r{5/2; 5} and Wythoff symbol 5/25|2. Its faces are 12{5/2}+30{4}+12{5}.

The rhombidodecadodecahedron is implemented in the Wolfram Language as UniformPolyhedron[76], UniformPolyhedron["Rhombidodecadodecahedron"], UniformPolyhedron[{"Coxeter", 48}], UniformPolyhedron[{"Kaleido", 42}], UniformPolyhedron[{"Uniform", 38}], or UniformPolyhedron[{"Wenninger", 76}]. It is also implemented in the Wolfram Language as PolyhedronData["Rhombidodecadodecahedron"].

The circumradius for unit edge length is

 R=1/2sqrt(7).

Its dual polyhedron is the medial deltoidal hexecontahedron.


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. "38: Rhombidodecadodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/38.html.Wenninger, M. J. "Rhombidodecadodecahedron." Model 76 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 116-117, 1989.

Referenced on Wolfram|Alpha

Rhombidodecadodecahedron

Cite this as:

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

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