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Small Ditrigonal Dodecicosidodecahedron

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U43

The small ditrigonal dodecicosidodecahedron is the uniform polyhedron with Maeder index 42 (Maeder 1997), Wenninger index 82 (Wenninger 1989), Coxeter index 55 (Coxeter et al. 1954), and Har'El index 48 (Har'El 1993). It has Wythoff symbol 35/3|5. Its faces are 20{3}+12{5/2}+12{10}.

The small ditrigonal dodecicosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[82], UniformPolyhedron["SmallDitrigonalDodecicosidodecahedron"], UniformPolyhedron[{"Coxeter", 55}], UniformPolyhedron[{"Kaleido", 48}], UniformPolyhedron[{"Uniform", 43}], or UniformPolyhedron[{"Wenninger", 82}].

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 ditrigonal dodecacronic hexecontahedron.

See also

Small Ditrigonal Dodecacronic Hexecontahedron, 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." Geom. Dedicata 47, 57-110, 1993. http://www.math.technion.ac.il/~rl/docs/uniform.pdf.Maeder, R. E. "43: Small Ditrigonal Dodecicosidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/43.html.Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, 1971.

Referenced on Wolfram|Alpha

Small Ditrigonal Dodecicosidodecahedron

Cite this as:

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

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