Great Icosicosidodecahedron


The great icosicosidodecahedron, not to be confused with the great icosahedron or great icosidodecahedron, is the uniform polyhedron with Maeder index 48 (Maeder 1997), Wenninger index 88 (Wenninger 1989), Coxeter index 62 (Coxeter et al. 1954), and Har'El index 53 (Har'El 1993). It has Wythoff symbol 3/25|3. Its faces are 20{3}+20{6}+12{5}.

The great icosicoidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[88], UniformPolyhedron["GreatIcosidodecahedron"], UniformPolyhedron[{"Coxeter", 62}], UniformPolyhedron[{"Kaleido", 53}], UniformPolyhedron[{"Uniform", 48}], or UniformPolyhedron[{"Wenninger", 88}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatIcosidodecahedron"].

Its convex hull is the truncated dodecahedron.


Its skeleton is the dodecicosahedral graph, illustrated above in a few embeddings.

Its circumradius for unit edge length is


Its dual is the great icosacronic hexecontahedron.

See also

Uniform Polyhedron

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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. "48: Great Icosicosidodecahedron." 1997., M. J. "Great Icosicosidodecahedron." Model 88 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 137-139, 1989.

Referenced on Wolfram|Alpha

Great Icosicosidodecahedron

Cite this as:

Weisstein, Eric W. "Great Icosicosidodecahedron." From MathWorld--A Wolfram Web Resource.

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