Truncated Icosahedron

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

An Archimedean Solid used in the construction of Soccer Balls. Its Dual Polyhedron is the Pentakis Dodecahedron. It has Schläfli Symbol t $\{3,5\}$ . It is also Uniform Polyhedron $U_{25}$ and has Wythoff Symbol $2\,5\,\vert\,3$ . Its faces are $20\{6\}+12\{5\}$ . The Inradius, Midradius, and Circumradius for are

$\displaystyle r$	$\textstyle =$	$\displaystyle {\textstyle{9\over 872}}(21+\sqrt{5}\,)\sqrt{58+18\sqrt{5}} \approx 2.37713$
$\displaystyle \rho$	$\textstyle =$	$\displaystyle {\textstyle{3\over 4}}(1+\sqrt{5}\,) \approx 2.42705$
$\displaystyle R$	$\textstyle =$	$\displaystyle {\textstyle{1\over 4}}\sqrt{58+18\sqrt{5}} \approx 2.47802.$