Now all that we need to do is to shift back  by same vector  that brought cell to (approximately) center of the lattice.
We are almost done. We still have to check if  is inside the lattice. If this is not the case we need to shift it back to the lattice but now we are allowed to use only a vector whose components are multiples of lattice dimensions (and we can safely restrict to +1 and -1 multiples of the lattice dimmensions) . For example we may have:
 where  ,  ,  are dimensions of the lattice.
There is no cheating here. In the lattice with periodic boundary conditions you are allowed to shift point coordinates a vector whose components are multiples of lattice dimensions.
All we need to do is to examine new center of mass position and form suitable vector  .
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