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Small Ditrigonal Icosidodecahedron


U30

The small ditrigonal icosidodecahedron is the uniform polyhedron with Maeder index 30 (Maeder 1997), Weinninger index 70 (Wenninger 1971, p. 106-107), Coxeter index 39 (Coxeter et al. 1954), and Har'El index 35 (Har'El 1993). It has Wythoff symbol 3|35/2 and its faces are 20{3}+12{5/2}. A faceted version is the ditrigonal dodecadodecahedron.

SmallDitrigonalIcosidodecahedronAndDual

It is illustrated above together with its dual.

The small ditrigonal icosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[70], UniformPolyhedron["SmallDitrigonalIcosidodecahedron"], UniformPolyhedron[{"Coxeter", 39}], UniformPolyhedron[{"Kaleido", 35}], UniformPolyhedron[{"Uniform", 30}], or UniformPolyhedron[{"Wenninger", 70}].

DitrigonalIcosidodecahedralGraph

Its skeleton is the ditrigonal icosidodecahedral graph.

The convex hull of the small ditrigonal icosidodecahedron is a regular dodecahedron, whose dual is the icosahedron, so the dual of the great ditrigonal dodecicosidodecahedron (the small triambic icosahedron) is one of the icosahedron stellations (Wenninger 1983, p. 42).

Its circumradius for unit edge lengths is

 R=1/2sqrt(3).

Its dual polyhedron is the small triambic icosahedron.


See also

Small Triambic Icosahedron, 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. "30: Small Ditrigonal Icosidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/30.html.Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 106-107, 1971.Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, 1983.

Referenced on Wolfram|Alpha

Small Ditrigonal Icosidodecahedron

Cite this as:

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

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