What does anisomorphic mean?
Anisomorphic is an adjective meaning not isomorphic — that is, differing in form, structure, or shape. It arises most often in mathematics, where two algebraic structures such as groups, rings, or graphs are said to be anisomorphic when no structure-preserving one-to-one correspondence exists between them. The term also appears in crystallography and biology to describe objects or organisms whose forms differ markedly. Built from Greek roots — 'an-' (not), 'iso-' (equal), and 'morphē' (form) — it is essentially the negation of its far more common counterpart, isomorphic. Because it belongs to formal scientific vocabulary, it rarely appears outside academic writing, yet it serves a precise purpose: stating plainly that two things that might look comparable are, on careful analysis, structurally distinct. For students of mathematics or the natural sciences, recognizing when structures are anisomorphic is often as informative as finding when they match.
adjectiveNot isomorphic; differing in form, structure, or shape, especially in mathematics where two structures fail to correspond exactly under a structure-preserving mapping.
- Differing in form or structure; not corresponding in shape or organization.
- In mathematics, lacking an isomorphism between two algebraic or geometric structures.
"The two crystal lattices are anisomorphic, so no one-to-one correspondence exists between their atomic arrangements."
"The two graphs are anisomorphic because one contains a cycle of length three and the other does not."
"Under the microscope, the anisomorphic cells of the tissue showed clearly irregular shapes and sizes."
In mathematics, proving two groups are anisomorphic can be just as illuminating as proving they match — sometimes the mismatch reveals the deeper truth.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of anisomorphic
Anisomorphic derives from Greek elements: the negative prefix 'an-', the combining form 'iso-' (from 'isos', meaning equal), and 'morphē' (form or shape), giving it the literal sense of 'not equal in form'. It was formed on the model of 'isomorphic', which entered scientific English during the nineteenth century alongside the rise of structural comparison in chemistry, crystallography, and later abstract algebra. Related words sharing the same 'morphē' root include morphology, amorphous, and anthropomorphic.
How anisomorphic is actually used
A technical term used chiefly in mathematics, crystallography, and the sciences; rare in everyday language and almost always found in formal or academic contexts.
Easily confused with anisomorphic
Isomorphic describes structures that correspond exactly under a structure-preserving map, whereas anisomorphic describes those that do not.
Anisotropic refers to materials whose physical properties vary with direction, while anisomorphic refers to a lack of structural or formal correspondence.