- In geometry, an isomorphism is a transformation that doesn't alter the side-lengths and the angle sizes of the figure
involved. Examples of such transformations include reflections, rotations,
translations, or transformations by a glide. In set
theory, an isomorphism is a one-to-one correspondence between the elements of two sets such that the result
of an operation on elements of one set corresponds to the result of
the analogous operation on their images in the other set.
- In crystallography, isomorphism is the formation by different compounds of minerals
of crystals have closely similar external
forms and lattice structure. Isomorphous compounds have similar chemical composition – ions of similar size, charge, and electrical polarizability being substituted
for each other – and form mixed crystals.