Great Rhombicosidodecahedron (Archimedean)

$\begin{figure}\begin{center}\BoxedEPSF{Great_Rhombicosidodec_net.epsf}\end{center}\end{figure}$

An Archimedean Solid also known as the Rhombitruncated Icosidodecahedron. It is sometimes improperly called the Truncated Icosidodecahedron, a name which is inappropriate since Truncation would yield Rectangular instead of Square. The great rhombicosidodecahedron is also Uniform Polyhedron $U_{28}$ . Its Dual is the Disdyakis Triacontahedron, also called the Hexakis Icosahedron. It has Schläfli Symbol t $\left\{{3\atop 5}\right\}$ and Wythoff Symbol $2\,3\,5\,\vert$ . The Inradius, Midradius, and Circumradius for are

$\displaystyle r$	$\textstyle =$	$\displaystyle {\textstyle{1\over 241}}(105+6\sqrt{5}\,)\sqrt{31+12\sqrt{5}}\approx 3.73665$
$\displaystyle \rho$	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}\sqrt{30+12\sqrt{5}}\approx 3.76938$
$\displaystyle R$	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}\sqrt{31+12\sqrt{5}}\approx 3.80239.$

References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 137, 1987.