Snub Icosidodecadodecahedron

$\begin{figure}\begin{center}\BoxedEPSF{U46.epsf scaled 700}\end{center}\end{figure}$

The Uniform Polyhedron $U_{46}$ whose Dual Polyhedron is the Medial Hexagonal Hexecontahedron. It has Wythoff Symbol $\vert\,3\,{\textstyle{5\over 3}}\,5$ . Its faces are $12\{{\textstyle{4\over 2}}\}+80\{3\}+12\{5\}$ . It has Circumradius for of

$\displaystyle R$	$\textstyle =$	$\displaystyle {1\over 2}\sqrt{2^{4/3}-14x+2^{2/3}x^2\over 2^{4/3}-8x+2^{2/3}x^2}$
	$\textstyle =$	$\displaystyle 1.12689791279994\ldots,$

where

$\begin{displaymath} x=(25+3\sqrt{69}\,)^{1/3}. \end{displaymath}$

References

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 177-178, 1971.