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Snub Icosidodecadodecahedron

\begin{figure}\begin{center}\BoxedEPSF{U46.epsf scaled 700}\end{center}\end{figure}

The Uniform Polyhedron $U_{46}$ whose Dual Polyhedron is the Medial Hexagonal Hexecontahedron. It has Wythoff Symbol $\vert\,3\,{\textstyle{5\over 3}}\,5$. Its faces are $12\{{\textstyle{4\over 2}}\}+80\{3\}+12\{5\}$. It has Circumradius for $a=1$ of

$\displaystyle R$ $\textstyle =$ $\displaystyle {1\over 2}\sqrt{2^{4/3}-14x+2^{2/3}x^2\over 2^{4/3}-8x+2^{2/3}x^2}$  
  $\textstyle =$ $\displaystyle 1.12689791279994\ldots,$  

where

\begin{displaymath}
x=(25+3\sqrt{69}\,)^{1/3}.
\end{displaymath}


References

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 177-178, 1971.




© 1996-9 Eric W. Weisstein
1999-05-26