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2007 AMC 12A Question 20

AMC12 · 2007 AMC 12A

Question 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?
  1. $\dfrac{5\sqrt2-7}{3}$
  2. $\dfrac{10-7\sqrt2}{3}$
  3. $\dfrac{3-2\sqrt2}{3}$
  4. $\dfrac{8\sqrt2-11}{3}$
  5. $\dfrac{6-4\sqrt2}{3}$