Icositruncated Dodecadodecahedron


The icositruncated dodecadodecahedron, also called the icosidodecatruncated icosidodecahedron, is the uniform polyhedron with Maeder index 45 (Maeder 1997), Wenninger index 84 (Wenninger 1989), Coxeter index 57 (Coxeter et al. 1954), and Har'El index 50 (Har'El 1993). It has Wythoff symbol 35/35| and faces 20{6}+12{10}+12{(10)/3}.

The icositruncated dodecadodecahedron is implemented in the Wolfram Language as UniformPolyhedron[84], UniformPolyhedron["IcositruncatedDodecadodecahedron"], UniformPolyhedron[{"Coxeter", 57}], UniformPolyhedron[{"Kaleido", 50}], UniformPolyhedron[{"Uniform", 45}], or UniformPolyhedron[{"Wenninger", 84}]. It is also implemented in the Wolfram Language as PolyhedronData["IcositruncatedDodecadodecahedron"].

Its circumradius for unit edge length is


Its dual polyhedron is the tridyakis icosahedron.

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. "45: Icositruncated Dodecadodecahedron." 1997., M. J. "Icositruncated Dodecadodecahedron." Model 84 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 130-131, 1989.

Referenced on Wolfram|Alpha

Icositruncated Dodecadodecahedron

Cite this as:

Weisstein, Eric W. "Icositruncated Dodecadodecahedron." From MathWorld--A Wolfram Web Resource.

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