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Great Inverted Snub Icosidodecahedron

\begin{figure}\begin{center}\BoxedEPSF{U69.epsf scaled 500}\end{center}\end{figure}

The Uniform Polyhedron $U_{69}$ whose Dual is the Great Inverted Pentagonal Hexecontahedron. It has Wythoff Symbol $\vert\,2\,3\,{\textstyle{5\over 2}}$. Its faces are $80\{3\}+12\{{\textstyle{5\over 2}}\}$. For unit edge length, it has Circumradius

$\displaystyle R$ $\textstyle =$ $\displaystyle {1\over 2}\sqrt{8\cdot 2^{2/3}-16x+2^{1/3} x^2\over 8\cdot 2^{2/3}-10x+2^{1/3}x^2}$  
  $\textstyle =$ $\displaystyle 0.816080674799923,$  


x\equiv \left({49-27\sqrt{5}+3\sqrt{6}\sqrt{93-49\sqrt{5}}\,}\right)^{1/3}.


Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, p. 179, 1989.

© 1996-9 Eric W. Weisstein