AMC 12A 2007 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?

Answer Choices
A. \dfrac{5 \sqrt{2}-7}{3}
B. \dfrac{10-7 \sqrt{2}}{3}
C. \dfrac{3-2 \sqrt{2}}{3}
D. \dfrac{8 \sqrt{2}-11}{3}
E. \dfrac{6-4 \sqrt{2}}{3}