(Polar molecules, Non-polar molecules, etc.)
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Correct me if I'm wrong, but I believe square planar is the only VSEPR shape where the molecule may contain lone pairs and still be nonpolar (if every X in AX4E2 is the same element). In any other shape, lone pairs will indicate the net dipole does not cancel and therefore the molecule is polar. Many of the VSEPR shapes with no lone pairs are able to be nonpolar, such as linear, trigonal planar, and tetrahedral with the same elements bonded to the central atom.
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