Posted by Steve Simon on February 18, 2013, 10:14 pm, in reply to "FCCBCCequivalency"
It might help to build a model here. I think you are suggesting that the four points in the middle of the north, south, east, and west faces form a square (turned 45 degrees). But this does not become a cube when you consider the next unit cell above, because the height up to the next layer (which is the lattice constant a) is not the same as the edgelength of the square you just described (which is a/sqrt(2)). Does this help? 
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