isomorph

An isomorph can be seen in the crystal structures of these two different minerals.

Definition

Noun:
- A substance or object that is isomorphic to another: In crystallography and chemistry, an "isomorph" refers to a substance that crystallizes in the same form as another substance, with a similar atomic arrangement.
- A mathematical structure that is isomorphic to another: In mathematics, an "isomorph" is a structure (such as a group, ring, or graph) that has a one-to-one correspondence with another structure, preserving all relevant operations and properties.

Usage Examples

Noun:
- Calcite and aragonite are isomorphs of calcium carbonate. (Both substances have the same chemical formula but different crystal structures; here, "isomorph" indicates a structural similarity in a broader sense.)
- In group theory, the cyclic group of order 4 is an isomorph of the Klein four-group under certain mappings. (These groups are structurally identical in terms of group operations.)

Advanced Usage

"to be an isomorph of": to be structurally identical or functionally equivalent to something.
- The new software system is an isomorph of the older one, with the same features but a different interface. (The systems are functionally equivalent.)

Variants and Related Words

Isomorphic (adj): having the same form or structure; related by isomorphism.
- The two crystals are isomorphic, meaning they share the same external shape. (They have identical forms.)
Isomorphism (n): the state or property of being isomorphic; a one-to-one correspondence preserving structure.
- The isomorphism between the two graphs was proven by mapping vertices to vertices. (Structural identity between mathematical objects.)

Synonyms

Counterpart: a person or thing that corresponds to or has the same function as another.
Analogue: a thing that is similar or comparable to something else in certain respects.
Homologue: a thing that is similar in position, structure, or function (used in biology and chemistry).

Related Idioms

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