I am looking for a word to denote an element in a binary relation, which in itself would connote the duality of the relationship. For example, a binary relation is the one between the east and the west half of a sphere so we call each a hemisphere:
From Latin hemisphaerium, from Ancient Greek ἡμισφαίριον (hēmisphaírion), from ἡμι- (hēmi-, “half”) + σφαῖρα (sphaîra, “sphere”); hemi- + sphere
So I am looking for a more abstract/general word (that could be applied to something other than a sphere) that would indicate that the entity in question is one of the two sides in a binary relation and would like that word to unambiguously mean that (and remove the possibility of having more than two sides) and that it's not necessarily half because that implies a 50/50 split, which shouldn't be implied by that word.
Another example could be the word wife meaning (in a traditional sense) one of the two spouses in a marital binary relation: "the wife is a [X] of the marriage"