Understanding Cell Volume: Why It's Independent of Choice

[beman]

"Volume of a primitive cell is independent of the choice of the cell."
Why?

 

[M Quack]

Because, by definition, a cell is primitive if it contains exactly the smallest number of atoms possible (the smallest possible basis) from which the entire lattice can be constructed.

Once you have one possible primitive cell you can obtain others by cutting off a bit on one side and adding it on the opposite side. Obviously, this operation does not change the volume of the cell.