AMC 12 2007a Problem 20

Corners are sliced off a unit cube so that the six faces each become regular octagons. What is the total volume of the removed tetrahedra?

$\mathrm{(A)}\ \frac{5\sqrt{2}-7}{3} \mathrm{(B)}\ \frac{10-7\sqrt{2}}{3} \mathrm{(C)}\ \frac{3-2\sqrt{2}}{3} \mathrm{(D)}\ \frac{8\sqrt{2}-11}{3} \mathrm{(E)}\ \frac{6-4\sqrt{2}}{3}$