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Small Retrosnub Icosicosidodecahedron

\begin{figure}\begin{center}\BoxedEPSF{U72.epsf scaled 600}\end{center}\end{figure}

The Uniform Polyhedron $U_{72}$ also called the Small Inverted Retrosnub Icosicosidodecahedron whose Dual Polyhedron is the Small Hexagrammic Hexecontahedron. It has Wythoff Symbol $\vert\,{\textstyle{3\over 2}}\,{\textstyle{3\over 2}}\,{\textstyle{5\over 2}}$. Its faces are $100\{3\}+12\{{\textstyle{5\over 2}}\}$. It has Circumradius with $a=1$

$\displaystyle R$ $\textstyle =$ $\displaystyle {\textstyle{1\over 4}}\sqrt{13+3\sqrt{5}-\sqrt{102+46\sqrt{5}}}$  
  $\textstyle \approx$ $\displaystyle 0.580694800133921 .$  


Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 194-199, 1971.

© 1996-9 Eric W. Weisstein