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I'm struggling in identifying the lattice points and atom basis.

As I understand in a cube, there are 8 lattice points, on on each corner of a cube. But in 2d it is any square between 4 points which are the lattice points. Is this correct?

So if the points on the corners are the lattice points. What confuses me is that a primitive cell can only have 1 lattice point and so if it's a square I thought it would have four lattice points not one.

Also I don't understand how to define a basis with each lattice point?

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# Lattice points and lattice basis

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