Truncated Dodecahedron

$\begin{figure}\begin{center}\BoxedEPSF{Truncated_Dodecahedron_net.epsf scaled 800}\end{center}\end{figure}$

An Archimedean Solid whose Dual Polyhedron is the Triakis Icosahedron. It has Schläfli Symbol t $\{5,3\}$ . It is also Uniform Polyhedron $U_{26}$ and has Wythoff Symbol $2\,3\,\vert\,5$ . Its faces are $20\{3\}+12\{10\}$ . The Inradius, Midradius, and Circumradius for are

$\displaystyle r$	$\textstyle =$	$\displaystyle {\textstyle{5\over 488}}(17\sqrt{2}+3\sqrt{10}\,)\sqrt{37+15\sqrt{5}} \approx 2.88526$
$\displaystyle \rho$	$\textstyle =$	$\displaystyle {\textstyle{1\over 4}}(5+3\sqrt{5}\,) \approx 2.92705$
$\displaystyle R$	$\textstyle =$	$\displaystyle {\textstyle{1\over 4}}\sqrt{74+30\sqrt{5}} \approx 2.96945.$