TOPICS
Search

Snub Icosidodecadodecahedron

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
U46

The snub icosidodecadodecahedron is the uniform polyhedron with Maeder index 46 (Maeder 1997), Wenninger index 112 (Wenninger 1989), Coxeter index 58 (Coxeter et al. 1954), and Har'El index 51 (Har'El 1993). It has Wythoff symbol |35/35 and faces 12{4/2}+80{3}+12{5}.

The snub icosidodecadodecahedron is implemented in the Wolfram Language as UniformPolyhedron[112], UniformPolyhedron["SnubIcosidodecadodecahedron"], UniformPolyhedron[{"Coxeter", 58}], UniformPolyhedron[{"Kaleido", 51}], UniformPolyhedron[{"Uniform", 46}], or UniformPolyhedron[{"Wenninger", 112}]. It is also implemented in the Wolfram Language as PolyhedronData["SnubIcosidodecadodecahedron"].

It has circumradius for unit edge length of

R=1/2sqrt((2^(4/3)-14x+2^(2/3)x^2)/(2^(4/3)-8x+2^(2/3)x^2))
(1)
=1/2sqrt((2P-1)/(P-1))
(2)
=(64x^6-128x^4+68x^2-11)_2
(3)
=1.12689791279994...,
(4)

where

x=(25+3sqrt(69))^(1/3)
(5)

and P is the plastic constant.

Its dual polyhedron is the medial hexagonal hexecontahedron.

See also

Plastic Constant, Uniform Polyhedron

Portions of this entry contributed by Tito Piezas III

Explore with Wolfram|Alpha

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. "46: Snub Icosidodecadodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/46.html.Wenninger, M. J. "Snub Icosidodecadodecahedron." Model 112 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 177-178, 1971.

Referenced on Wolfram|Alpha

Snub Icosidodecadodecahedron

Cite this as:

Piezas, Tito III and Weisstein, Eric W. "Snub Icosidodecadodecahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SnubIcosidodecadodecahedron.html

Subject classifications