Truncated Cube

$\begin{figure}\BoxedEPSF{Truncated_Cube_net.epsf scaled 800}\end{figure}$

An Archimedean Solid whose Dual Polyhedron is the Triakis Octahedron. It has Schläfli Symbol t $\{4,3\}$ . It is also Uniform Polyhedron and has Wythoff Symbol $2\,3\,\vert\,4$ . Its faces are $8\{3\}+6\{8\}$ . The Inradius, Midradius, and Circumradius for are

$\displaystyle r$	$\textstyle =$	$\displaystyle {\textstyle{1\over 17}}(5+2\sqrt{2}\,)\sqrt{7+4\sqrt{2}} \approx 1.63828$
$\displaystyle \rho$	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}(2+\sqrt{2}\,) \approx 1.70711$
$\displaystyle R$	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}\sqrt{7+4\sqrt{2}} \approx 1.77882.$

References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 138, 1987.