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Rhombicosahedron


U56

The rhombicosahedron is the uniform polyhedron with Maeder index 56 (Maeder 1997), Wenninger index 96 (Wenninger 1989), Coxeter index 72 (Coxeter et al. 1954), and Har'El index 61 (Har'El 1993). It has Wythoff symbol 25/23| and its faces are 10{6}+15{4}+15{4/3}+10{6/5}.

The rhombicosahedron is implemented in the Wolfram Language as UniformPolyhedron[96], UniformPolyhedron["Rhombicosahedron"], UniformPolyhedron[{"Coxeter", 72}], UniformPolyhedron[{"Kaleido", 61}], UniformPolyhedron[{"Uniform", 56}], or UniformPolyhedron[{"Wenninger", 96}]. It is also implemented in the Wolfram Language as PolyhedronData["Rhombicosahedron"].

The circumradius for unit edge length is

 R=1/2sqrt(7).

Its dual polyhedron is the rhombicosacron.


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. "56: Rhombicosahedron." 1997. https://www.mathconsult.ch/static/unipoly/56.html.Wenninger, M. J. "Rhombicosahedron." Model 96 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 149-150, 1971.

Referenced on Wolfram|Alpha

Rhombicosahedron

Cite this as:

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

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