Is there a quick way to determine if a salt (or ionic compound in general) crystal should be birefringent from its formula without having to know/look up the crystal structure? When I'm looking for protein crystals, if I know the condition has a lot of salt in it, but it shouldn't be birefringent (e.g. NaCl), it's a hint that birefringent crystals I do see might be protein.
Is the only non-birefringent crystal type (e.g. not glasses) cubic? Does it matter if it's primitive, face-centered, or body-centered?
Back to looking for a generalization, are most (all?) salts with polyatomic ions birefringent? All +1/-1 (NaCl, KBr, etc...) aren't?