Great Cubicuboctahedron

The Uniform Polyhedron $U_{14}$ whose Dual Polyhedron is the Great Hexacronic Icositetrahedron. It has Wythoff Symbol $3\,4\,\vert\,{\textstyle{4\over 3}}$. Its faces are $8\{3\}+6\{4\}+6\{{\textstyle{8\over 3}}\}$. It is a Faceted version of the Cube. The Circumradius of a great cubicuboctahedron with unit edge length is

$$R={\textstyle{1\over 2}}\sqrt{5-2\sqrt{2}}\,.$$

References

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 118-119, 1989.