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Small Dodecicosahedron

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U50

The small dodecicosahedron is the uniform polyhedron with Maeder index 50 (Maeder 1997), Wenninger index 90 (Wenninger 1989), Coxeter index 64 (Coxeter et al. 1954), and Har'El index 55 (Har'El 1993). It has Wythoff symbol 3/235| and its faces are 20{6}+12{10}.

The small dodecicosahedron is implemented in the Wolfram Language as UniformPolyhedron[90], UniformPolyhedron["SmallDodecicosahedron"], UniformPolyhedron[{"Coxeter", 64}], UniformPolyhedron[{"Kaleido", 55}], UniformPolyhedron[{"Uniform", 50}], or UniformPolyhedron[{"Wenninger", 90}]. It is also implemented in the Wolfram Language as PolyhedronData["SmallDodecicosahedron"].

DodecicosahedralGraph

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

Its circumradius for unit edge lengths is

R=1/4sqrt(34+6sqrt(5)).

Its dual polyhedron is the small dodecicosacron.

See also

Small Dodecicosacron, 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. "90: Small Dodecicosahedron." 1997. https://www.mathconsult.ch/static/unipoly/50.html.Wenninger, M. J. "Small Dodecicosahedron." Model XX in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 141-142, 1971.

Referenced on Wolfram|Alpha

Small Dodecicosahedron

Cite this as:

Weisstein, Eric W. "Small Dodecicosahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SmallDodecicosahedron.html

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