Small Retrosnub Icosicosidodecahedron

$\begin{figure}\begin{center}\BoxedEPSF{U72.epsf scaled 600}\end{center}\end{figure}$

The Uniform Polyhedron $U_{72}$ also called the Small Inverted Retrosnub Icosicosidodecahedron whose Dual Polyhedron is the Small Hexagrammic Hexecontahedron. It has Wythoff Symbol $\vert\,{\textstyle{3\over 2}}\,{\textstyle{3\over 2}}\,{\textstyle{5\over 2}}$ . Its faces are $100\{3\}+12\{{\textstyle{5\over 2}}\}$ . It has Circumradius with

$\displaystyle R$	$\textstyle =$	$\displaystyle {\textstyle{1\over 4}}\sqrt{13+3\sqrt{5}-\sqrt{102+46\sqrt{5}}}$
	$\textstyle \approx$	$\displaystyle 0.580694800133921 .$

References

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 194-199, 1971.