Great Icosidodecahedron

$\begin{figure}\begin{center}\BoxedEPSF{U54.epsf scaled 700}\end{center}\end{figure}$

A Uniform Polyhedron $U_{54}$ whose Dual is the Great Rhombic Triacontahedron (also called the Great Stellated Triacontahedron). It is a Stellated Archimedean Solid. It has Schläfli Symbol $\left\{{3\atop{\textstyle{5\over 2}}}\right\}$ and Wythoff Symbol $2\,\vert\,3\,{\textstyle{5\over 2}}$ . Its faces are $20\{3\}+12\{{\textstyle{5\over 2}}\}$ . Its Circumradius for unit edge length is

$\begin{displaymath} R=\phi^{-1}, \end{displaymath}$

where $\phi$ is the Golden Ratio.

References

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 124, 1989.

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, p. 147, 1989.