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Small Rhombicosidodecahedron

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

An Archimedean Solid whose Dual Polyhedron is the Deltoidal Hexecontahedron. It has Schläfli Symbol r $\left\{{3\atop 5}\right\}$. It is also Uniform Polyhedron $U_{27}$ with Wythoff Symbol $3\,5\,\vert\,2$. Its faces are $20\{3\}+30\{4\}+12\{5\}$. The Small Dodecicosidodecahedron and Small Rhombidodecahedron are Faceted versions. The Inradius, Midradius, and Circumradius for $a=1$ are

$\displaystyle r$ $\textstyle =$ $\displaystyle {\textstyle{1\over 41}}(15+2\sqrt{5}\,)\sqrt{11+4\sqrt{5}} = 2.12099\ldots$  
$\displaystyle \rho$ $\textstyle =$ $\displaystyle {\textstyle{1\over 2}}\sqrt{10+4\sqrt{5}} = 2.17625\ldots$  
$\displaystyle R$ $\textstyle =$ $\displaystyle {\textstyle{1\over 2}}\sqrt{11+4\sqrt{5}} = 2.23295\ldots.$  

See also Great Rhombicosidodecahedron (Archimedean), Great Rhombicosidodecahedron (Uniform)

© 1996-9 Eric W. Weisstein