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I think polydentates do affect shape of coordination compounds because they offer more than one binding site. For example, since en has two binding sites, it will increase the coordination compound by 2
They are correct above that chelating ligands effect the shape of a coordination compound. Yes, we use the coordination number of the central metal to determine the shape; but a bidentate or tridentate ligand would raise the coordination compound by 2 or 3 respectively.
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