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Great Snub Icosidodecahedron

\begin{figure}\begin{center}\BoxedEPSF{U57.epsf scaled 700}\end{center}\end{figure}

The Uniform Polyhedron $U_{57}$ whose Dual is the Great Pentagonal Hexecontahedron. It has Wythoff Symbol $\vert\,2\,3\,{\textstyle{5\over 3}}$. Its faces are $80\{3\}+12\{{\textstyle{5\over 2}}\}$. For unit edge length, it has Circumradius

R={\textstyle{1\over 2}}\sqrt{2-x\over 1-x}\approx 0.6450202,

where $x$ is the most Negative Root of


with $\phi$ the Golden Ratio.


Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 186-188, 1989.

© 1996-9 Eric W. Weisstein