Great Inverted Snub Icosidodecahedron

$\begin{figure}\begin{center}\BoxedEPSF{U69.epsf scaled 500}\end{center}\end{figure}$

The Uniform Polyhedron $U_{69}$ whose Dual is the Great Inverted Pentagonal Hexecontahedron. It has Wythoff Symbol $\vert\,2\,3\,{\textstyle{5\over 2}}$ . Its faces are $80\{3\}+12\{{\textstyle{5\over 2}}\}$ . For unit edge length, it has Circumradius

$\displaystyle R$	$\textstyle =$	$\displaystyle {1\over 2}\sqrt{8\cdot 2^{2/3}-16x+2^{1/3} x^2\over 8\cdot 2^{2/3}-10x+2^{1/3}x^2}$
	$\textstyle =$	$\displaystyle 0.816080674799923,$

where

$\begin{displaymath} x\equiv \left({49-27\sqrt{5}+3\sqrt{6}\sqrt{93-49\sqrt{5}}\,}\right)^{1/3}. \end{displaymath}$

References

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, p. 179, 1989.