Great Retrosnub Icosidodecahedron

The Uniform Polyhedron $U_{74}$, also called the Great Inverted Retrosnub Icosidodecahedron, whose Dual is the Great Pentagrammic Hexecontahedron. It has Wythoff Symbol $\vert\,2\,{\textstyle{3\over 2}}\,{\textstyle{5\over 3}}$. Its faces are $80\{3\}+12\{{\textstyle{5\over 2}}\}$. For unit edge length, it has Circumradius

$$R={\textstyle{1\over 2}}\sqrt{2-x\over 1-x}\approx 0.5800015,$$

where $x$ is the smaller Negative root of

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

with $\phi$ the Golden Mean.

References

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 189-193, 1989.