Great Truncated Icosidodecahedron

$\begin{figure}\begin{center}\BoxedEPSF{U68.epsf scaled 700}\end{center}\end{figure}$

The Uniform Polyhedron $U_{68}$ , also called the Great Quasitruncated Icosidodecahedron, whose Dual is the Great Disdyakis Triacontahedron. It has Schläfli Symbol t' $\left\{{3\atop{\textstyle{5\over 2}}}\right\}$ and Wythoff Symbol $2\,3\,{\textstyle{5\over 3}}\,\vert$ . Its faces are $20\{6\}+30\{4\}+12\{{\textstyle{10\over 3}}\}$ . Its Circumradius for unit edge length is

$\begin{displaymath} R={\textstyle{1\over 2}}\sqrt{31-12\sqrt{5}}\,. \end{displaymath}$

References

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 166-167, 1989.