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Are centre of symmetry(COS) and alternate axis of symmetry(AAOS) dependent on each other?

COS=Centre of symmetery AAOS=Alternate axis of symmetry Lets suppose a molecule has a COS. Does it need to have AAOS? What about the converse? If a molecule has AAOS does it necessarily have a COS? ...
PRITIPRIYA DASBEHERA's user avatar