Exceptional isomorphism

In mathematics, an exceptional isomorphism, also called an accidental isomorphism, is an isomorphism between members a_i and b_j of two families (usually infinite) of mathematical objects, that is not an example of a pattern of such isomorphisms. These coincidences are at times considered a matter of trivia, but in other respects they can give rise to other phenomena, notably exceptional objects. In the below, coincidences are listed in all places they occur.