They are both lattices, i.e., all the vectors are in the form of $m \vec{e}_1 + n\vec{e}_2 $ with $m$, $n$ integral. The point groups are the same, i.e., D2 In which sense are they different? A primitive cell vs a composite cell?

If there would be magnetic monopoles somewhere, such a way to bring Maxwell equations in a symmetric way, there should be a law of force describing the movement of such particles. If we imagine something similar to Lorentz force \begin{equation} \vec F = q_m \vec B \end{equation} then, the force ...