TOPICS
Search

Small Icosicosidodecahedron


U31

The smallI icosicosidodecahedron is the uniform polyhedron with Maeder index 31 (Maeder 1997), Wenninger index 71 (Wenninger 1989), Coxeter index 40 (Coxeter et al. 1954), and Har'El index 36 (Har'El 1993). It has Wythoff symbol 35/2|3 and its faces are 20{3}+20{6}+12{5/2}.

The smallI icosicosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[71], UniformPolyhedron["SmallIcosicosidodecahedron"], UniformPolyhedron[{"Coxeter", 40}], UniformPolyhedron[{"Kaleido", 36}], UniformPolyhedron[{"Uniform", 31}], or UniformPolyhedron[{"Wenninger", 71}]. It it also implemented in the Wolfram Language as PolyhedronData["SmallIcosicosidodecahedron"].

DodecicosahedralGraph

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

Its circumradius for unit edge lengths is

 R=sqrt((17+3sqrt(5))/2).

Its dual polyhedron is the small icosacronic hexecontahedron.


See also

Small Icosacronic Hexecontahedron, Uniform Polyhedron

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. "31: Small Icosicosidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/31.html.Wenninger, M. J. "Small Icosicosidodecahedron." Model 71 in Polyhedron Models. Cambridge, England: Cambridge University Press, p. 108, 1971.

Referenced on Wolfram|Alpha

Small Icosicosidodecahedron

Cite this as:

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

Subject classifications