Small Stellated Truncated Dodecahedron

The Uniform Polyhedron $U_{58}$ also called the Quasitruncated Small Stellated Dodecahedron whose Dual Polyhedron is the Great Pentakis Dodecahedron. It has Schläfli Symbol t' $\{{\textstyle{5\over 2}}, 5\}$ and Wythoff Symbol $2\,5\,\vert\,{\textstyle{5\over 3}}$. Its faces are $12\{5\}+12\{{\textstyle{10\over 3}}\}$. Its Circumradius with $a=1$ is

$$R={\textstyle{1\over 4}}\sqrt{34-10\sqrt{5}}\,.$$

References

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, p. 151, 1971.