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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 $a=1$ are

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

© 1996-9 Eric W. Weisstein