Great Snub Icosidodecahedron

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

$$x^3+2x^2-\phi^{-2}=0,$$

with $\phi$ the Golden Ratio.

References

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