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.