TOPICS
Search

Quasirhombicosidodecahedron


U67

The quasirhombicosidodecahedron is the uniform polyhedron with Maeder index 67 (Maeder 1997), Wenninger index 105 (Wenninger 1989), Coxeter index 84 (Coxeter et al. 1954), and Har'El index 72 (Har'El 1993). It has Schläfli symbol r'{3; 5/2} and Wythoff symbol 35/3|2. Its faces are 20{3}+30{4}+12{5/2}.

Unfortunately, some authors (e.g., Maeder 1997, Model 67) use the term "great rhombicosidodecahedron" to refer to this solid, despite the fact that the same term is commonly used (e.g., Cundy and Rowlett 1989, pp. 112-113) to refer to a distinct Archimedean solid.

The quasirhombicosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[105], UniformPolyhedron["GreatRhombicosidodecahedron"], UniformPolyhedron[{"Coxeter", 84}], UniformPolyhedron[{"Kaleido", 72}], UniformPolyhedron[{"Uniform", 67}], or UniformPolyhedron[{"Wenninger", 105}]. It is also implemented in the Wolfram Language as PolyhedronData["Quasirhombicosidodecahedron"].

SmallRhombicosidodecahedralGraph

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

Its dual is the great deltoidal hexecontahedron.

For unit edge length, its circumradius is

 R=1/2sqrt(11-4sqrt(5)).

See also

Rhombicosidodecahedron, 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.Cundy, H. and Rollett, A. "Great Rhombicosidodecahedron or Truncated Icosidodecahedron. 4.6.10." §3.7.12 in Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 112-113, 1989.Har'El, Z. "Uniform Solution for Uniform Polyhedra." Geometriae Dedicata 47, 57-110, 1993.Maeder, R. E. "67: Great Rhomibicosidodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/67.html.Wenninger, M. J. "Quasirhombicosidecahedron." Model 105 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 162-163, 1989.

Cite this as:

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

Subject classifications