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Great Rhombidodecahedron


U73

The great rhombidodecahedron is the uniform polyhedron with Maeder index 73 (Maeder 1997), Wenninger index 109 (Wenninger 1989), Coxeter index 89 (Coxeter et al. 1954), and Har'El index 78 (Har'El 1993). It has Wythoff symbol 25/3|3/2; 5/4| and faces are 30{4}+12{(10)/3}.

The great rhombidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[109], UniformPolyhedron["GreatRhombidodecahedron"], UniformPolyhedron[{"Coxeter",89 }], UniformPolyhedron[{"Kaleido", 78}], UniformPolyhedron[{"Uniform", 73}], or UniformPolyhedron[{"Wenninger", 109}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatRhombidodecahedron"].

SmallRhombicosidodecahedralGraph

Its skeleton is the small rhombicosidodecahedral graph.

Its circumradius for unit edge length is

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

Its dual is the great rhombidodecacron.


See also

Uniform Polyhedron

Explore with Wolfram|Alpha

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. "73: Great Rhombidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/73.html.Wenninger, M. J. "Great Rhombidodecahedron." Model 109 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 168-170, 1989.

Referenced on Wolfram|Alpha

Great Rhombidodecahedron

Cite this as:

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

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