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Great Icosihemidodecahedron


U71

The great icosihemidodecahedron is the uniform polyhedron with Maeder index 71 (Maeder 1997), Wenninger index 106 (Wenninger 1989), Coxeter index 85 (Coxeter et al. 1954), and Har'El index 76 (Har'El 1993). It has Wythoff symbol 3/23|5/3 and its faces are 20{3}+6{(10)/3}.

The great icosihemidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[106], UniformPolyhedron["GreatIcosihemidodecahedron"], UniformPolyhedron[{"Coxeter", 85}], UniformPolyhedron[{"Kaleido", 76}], UniformPolyhedron[{"Uniform", 71}], or UniformPolyhedron[{"Wenninger", 106}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatIcosihemidodecahedron"].

Its convex hull is the regular icosidodecahedron, and its vertices are those of the octahedron 5-compound.

IcosidodecahedralGraph

Its skeleton is the icosidodecahedral graph.

For unit edge length, its circumradius is

 R=phi^(-1),

where phi is the golden ratio.

Its dual is the great icosihemidodecacron.


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. "71: Great Icosihemidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/71.html.Wenninger, M. J. "Great Icosihemidodecahedron." Model 106 in Polyhedron Models. Cambridge, England: Cambridge University Press, p. 164, 1989.

Referenced on Wolfram|Alpha

Great Icosihemidodecahedron

Cite this as:

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

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