Small Icosicosidodecahedron

The Uniform Polyhedron $U_{31}$ whose Dual Polyhedron is the Small Icosacronic Hexecontahedron. It has Wythoff Symbol ${\textstyle{5\over 4}}\,5\,\vert\,5$. Its faces are $12\{5\}+6\{10\}$. Its Circumradius with $a=1$ is

$$R=\phi={\textstyle{1\over 2}}(1+\sqrt{5}\,),$$

where $\phi$ is the Golden Ratio.

References

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, p. 143, 1971.