symmetriin
Symmetriin is a term used in theoretical discussions to denote a class of symmetry-related invariants defined with respect to a specified transformation group. In this framework, a structure S is said to be symmetriin with respect to a group G if applying any transformation g in G to S leaves a designated feature F(S) unchanged. The group G is called the symmetriin group of S, and the corresponding invariants form the symmetriin class of S.
Origin and usage: The term is not part of standard mathematical nomenclature and appears in some speculative
Examples: A circle in the plane has a large symmetriin group—the full orthogonal group O(2)—preserving distance
Relation to symmetry: Symmetriin emphasizes invariants under a chosen group, akin to invariants studied in group
Applications: In design and computer graphics, symmetriin thinking helps create patterns invariant under specific operations; in
See also: symmetry, invariant, symmetry group, invariant theory, dihedral group, isometry.