in biology, a discontinuous genetic variation resulting in the occurrence of several different forms or types of individuals among the members of a single species. A discontinuous genetic variation divides the individuals of a population into two or more sharply distinct forms. The most obvious example of this is the separation of most higher organisms into male and female sexes. Another example is the different blood types in humans. In continuous variation, by contrast, the individuals do not fall into sharp classes but instead are almost imperceptibly graded between wide extremes. Examples include the smooth graduation of height among individuals of human populations and the graduations possible between the different geographic races. If the frequency of two or more discontinuous forms within a species is too high to be explained by mutation, the variation—as well as the population displaying it—is said to be polymorphic.

A polymorphism that persists over many generations is usually maintained because no one form possesses an overall advantage or disadvantage over the others in terms of natural selection. Some polymorphisms have no visible manifestations and require biochemical techniques to identify the differences that occur between the chromosomes, proteins, or DNA of different forms. The castes that occur in social insects are a special form of polymorphism that is attributable to differences in nutrition rather than to genetic variations.

in crystallography, the condition in which a solid chemical compound exists in more than one crystalline form; the forms differ somewhat in physical and, sometimes, chemical properties, although their solutions and vapours are identical. The existence of different crystalline or molecular forms of elements is called allotropy, although it has been suggested that the meaning of allotropy should be restricted to different molecular forms of an element, such as oxygen (O₂) and ozone (O₃), and that polymorphism be applied to different crystalline forms of the same species, whether a compound or an element. Differences in the crystalline forms of many elements and compounds were discovered during the 1820s by Eilhardt Mitscherlich, a German chemist.

Among polymorphs of certain compounds, one is more stable than the others under all conditions; in the cases of other compounds, one polymorph is stable within a particular range of temperature and pressure while another is stable under a different set of conditions. In either circumstance, the rate at which a less stable polymorph becomes more stable often is so low that an intrinsically unstable form may persist indefinitely. As an example of the first class, calcium carbonate has an orthorhombic form (i.e., having three unequal crystalline axes at right angles to each other) called aragonite and a hexagonal form (having three equal axes intersecting at angles of 60 degrees and a fourth axis at right angles to these three) called calcite. Calcite is the stabler form; aragonite changes into calcite rapidly at temperatures around 470° C (about 880° F) but very slowly at room temperatures. The second class is represented by silica, which has three forms—quartz, tridymite, and cristobalite—each of which is stable only in its particular range of temperature and pressure, the others slowly changing into the stable modification.

The conditions under which synthetic crystalline substances are prepared often dictate the formation of one or another polymorph; in the manufacture of pigments, particular care is required because the colour, reflectivity, and opacity frequently vary among the polymorphic modifications of a single substance.