Rhombidodecadodecahedron

The Uniform Polyhedron $U_{38}$ whose Dual Polyhedron is the Medial Deltoidal Hexecontahedron. It has Schläfli Symbol r $\left\{{{\textstyle{5\over 2}}\atop 5}\right\}$ and Wythoff Symbol ${\textstyle{5\over 2}}\,5\,\vert\,2$. Its faces are $12\{{\textstyle{5\over 2}}\}+30\{4\}+12\{5\}$. The Circumradius for unit edge length is

$$R={\textstyle{1\over 2}}\sqrt{7}\,.$$

References

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 116-117, 1989.