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# Great Ditrigonal Icosidodecahedron

2023-08-30

The great ditrigonal icosidodecahedron is the uniform polyhedron with Maeder index 47 (Maeder 1997), Wenninger index 87 (Wenninger 1989), Coxeter index 58 (Coxeter et al. 1954), and Har'El index 51 (Har'El 1993). It has Wythoff symbol and its faces are , and

The great ditrigonal icosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[87], UniformPolyhedron["GreatDitrigonal-Icosidodecahedron"], UniformPolyhedron["Coxeter", 58], UniformPolyhedron["Kaleido", 51], UniformPolyhedron["Uniform", 47], or UniformPolyhedron["Wenninger", 87]. It is also implemented in the Wolfram Language as PolyhedronData["GreatDitrigonalIcosidodecahedron"].

Its circumradius for unit edge length is

The convex hull of the great triambic icosahedron is a regular dodecahedron, whose dual is the icosahedron, so the dual of the great ditrigonal icosidodecahedron (the great triambic icosahedron) is one of the icosahedron stellations.

The cube 5-compound and tetrahedron 10-compound can be constructed from its vertices.

Its dual is the great 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." Geometriae Dedicata 47, 57-110, 1993.Maeder, R. E. "47: Great DitrigonalIcosidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/47.html.Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, p. 42, 1983.Wenninger, M. J. "Great Ditrigonal Icosidodecahedron." Model 87 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 135-136, 1989.

## Referenced on Wolfram|Alpha

Great Ditrigonal Icosidodecahedron

## Cite this as:

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