Small Dodecicosidodecahedron

$\begin{figure}\begin{center}\BoxedEPSF{U33.epsf scaled 700}\end{center}\end{figure}$

The Uniform Polyhedron $U_{33}$ whose Dual Polyhedron is the Small Dodecacronic Hexecontahedron. It has Wythoff Symbol ${\textstyle{3\over 2}}\,5\,\vert\,5$ . Its faces are $20\{3\}+12\{5\}+12\{10\}$ . It is a Faceted version of the Small Rhombicosidodecahedron. Its Circumradius with is

$\begin{displaymath} R={\textstyle{1\over 2}}\sqrt{11+4\sqrt{5}}\,. \end{displaymath}$

References

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 110-111, 1971.