Small Snub Icosicosidodecahedron

$\begin{figure}\begin{center}\BoxedEPSF{U32.epsf scaled 700}\end{center}\end{figure}$

The Uniform Polyhedron $U_{32}$ whose Dual Polyhedron is the Small Hexagonal Hexecontahedron. It has Wythoff Symbol $\vert\,3\,3\,{\textstyle{5\over 2}}$ (Har'El 1993 gives the symbol as $\vert\,{\textstyle{5\over 2}}\,3\,3$ .) Its faces are $100\{3\}+12\{{\textstyle{5\over 2}}\}$ . Its Circumradius for is

$\displaystyle R$	$\textstyle =$	$\displaystyle {\textstyle{1\over 4}}\sqrt{13+3\sqrt{5}+\sqrt{102+46\sqrt{5}}}$
	$\textstyle =$	$\displaystyle 1.4581903307387\ldots.$

References

Har'El, Z. ``Uniform Solution for Uniform Polyhedra.'' Geometriae Dedicata 47, 57-110, 1993.

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 172-173, 1971.