Great Ditrigonal Dodecicosidodecahedron

$\begin{figure}\begin{center}\BoxedEPSF{U42.epsf scaled 700}\end{center}\end{figure}$

The Uniform Polyhedron $U_{42}$ whose Dual is the Great Ditrigonal Dodecacronic Hexecontahedron. It has Wythoff Symbol $3\,5\,\vert\,{\textstyle{5\over 3}}$ . Its faces are $20\{3\}+12\{5\}+12\{{\textstyle{10\over 3}}\}$ , and its Circumradius for unit edge length is

$\begin{displaymath} R={\textstyle{1\over 4}}\sqrt{34-6\sqrt{5}}\,. \end{displaymath}$

References

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, p. 125, 1989.