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Small Rhombidodecahedron


U39

The small rhombidodecahedron is the uniform polyhedron with Maeder index 39 (Maeder 1997), Wenninger index 74 (Wenninger 1989), Coxeter index 46 (Coxeter et al. 1954), and Har'El index 44 (Har'El 1993). It has Wythoff symbol 25/25|. Its faces are 30{4}+12{10}. It is a faceted version of the small rhombicosidodecahedron

The small rhombidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[74], UniformPolyhedron["SmallRhombidodecahedron"], UniformPolyhedron[{"Coxeter", 46}], UniformPolyhedron[{"Kaleido", 44}], UniformPolyhedron[{"Uniform", 39}], or UniformPolyhedron[{"Wenninger", 74}]. It is also implemented in the Wolfram Language as PolyhedronData["SmallRhombidodecahedron"].

SmallRhombicosidodecahedralGraph

Ite skeleton is the small rhombicosidodecahedral graph, illustrated above in a few embeddings.

Its convex hull is a small rhombicosidodecahedron and its circumradius for unit edge lengths is

 R=1/2sqrt(11+4sqrt(5)).

Its dual polyhedron is the small rhombidodecacron.


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. "39: Small Rhombidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/39.html.Wenninger, M. J. "Small Rhombidodecahedron." Model 74 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 113-114, 1971.

Referenced on Wolfram|Alpha

Small Rhombidodecahedron

Cite this as:

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

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