Small Dodecahemicosahedron


The small dodecahemicosahedron is the uniform polyhedron with Maeder index 62 (Maeder 1997), Wenninger index 100 (Wenninger 1989), Coxeter index 78 (Coxeter et al. 1954), and Har'El index 67 (Har'El 1993). It has Wythoff symbol 5/35/2|3 and faces are 10{6}+12{5/2}. It is a faceted version of the icosidodecahedron.

The small dodecahemicosahedron is implemented in the Wolfram Language as UniformPolyhedron[100], UniformPolyhedron["SmallDodecahemicosahedron"], UniformPolyhedron[{"Coxeter", 78}], UniformPolyhedron[{"Kaleido", 67}], UniformPolyhedron[{"Uniform", 62}], or UniformPolyhedron[{"Wenninger", 100}]. It is also implemented in the Wolfram Language as PolyhedronData["SmallDodecahemicosahedron"].

Its convex hull is the regular icosidodecahedron.

Its skeleton is the dodecadodecahedral graph.

Its circumradius with unit edge length is


Its dual polyhedron is the small dodecahemicosacron.

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. "62: Small Dodecahemicosahedron." 1997., M. J. "Small Dodecahemicosahedron." Model 100 in Polyhedron Models. Cambridge, England: Cambridge University Press, p. 155, 1971.

Referenced on Wolfram|Alpha

Small Dodecahemicosahedron

Cite this as:

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

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