Changing Basis Vectors for FCC

Hi,

I am trying to figure out a way to change the basis vectors for the fcc lattice
given in the tutorial. 

Rather than having the primitive basis vectors pointing to the (1 1 0), (1 0 1),
(0 1 1) directions with length sqrt 0.5, I would like to instead define the
structure in terms of vectors that point along the body diagonal (1 1 1), (1 1
-2), and (-1 1 0) directions. 

These vectors, I am guessing are no longer primitive and when I do the
calculation, I do not get the same structure.

Best Regards,

Jeremy