Small Icosihemidodecahedron


The small icosihemidodecahedron is the uniform polyhedron with Maeder index 49 (Maeder 1997), Wenninger index 89 (Wenninger 1989), Coxeter index 63 (Coxeter et al. 1954), and Har'El index 54 (Har'El 1993). It has Wythoff symbol 3/23|5 and its faces are 20{3}+6{10}. It is a faceted version of the icosidodecahedron.

The small icosihemidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[89], UniformPolyhedron["Icosihemidodecahedron"], UniformPolyhedron[{"Coxeter", 63}], UniformPolyhedron[{"Kaleido", 54}], UniformPolyhedron[{"Uniform", 49}], or UniformPolyhedron[{"Wenninger", 89}]. It is also implemented in the Wolfram Language as PolyhedronData["Icosihemidodecahedron"].


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

Its circumradius for unit edge lengths is


Its convex hull is a regular icosidodecahedron and an octahedron 5-compound can be constructed from its vertices.

Its dual polyhedron is the small icosihemidodecacron.

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. "49: Small Icosihemidodecahedron." 1997., M. J. "Small Icosihemidodecahedron." Polyhedron Models. Cambridge, England: Cambridge University Press, p. 140, 1971.

Referenced on Wolfram|Alpha

Small Icosihemidodecahedron

Cite this as:

Weisstein, Eric W. "Small Icosihemidodecahedron." From MathWorld--A Wolfram Web Resource.

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