Nonkeysided

Nonkeysided is a neologism sometimes used in speculative discussions of geometry, combinatorics, and symmetry to describe a class of objects whose sides do not carry a fixed external key or label. In this sense, a nonkeysided polygon or shape is treated in an unlabeled form, where the identity of individual sides is not anchored to particular external keys. The concept emphasizes the relationships among sides and vertices rather than any prescribed correspondence to labeled keys.

In practical terms, a nonkeysided object has no canonical assignment of labels to its sides that must be preserved under transformations. This contrasts with keysided objects, where each side is associated with a specific key or label that remains attached under admissible symmetries. For example, a regular polygon with all sides indistinguishable is typically regarded as nonkeysided, while the same polygon with distinct labels on each side becomes keysided.

The term and idea are mainly used to discuss problems of unlabeled counting, symmetry, and automorphisms. They align with standard concerns in Polya enumeration and in the study of how many distinct shapes exist when side labels are ignored versus when they are fixed. Because nonkeysided is not a widely standardized term, some authors simply refer to unlabeled, symmetry-invariant, or label-agnostic objects or structures instead.

See also: unlabeled objects, symmetry, Polya enumeration, automorphism group. Note that nonkeysided is not an established designation in formal mathematics and may appear primarily in informal or fictional discussions about labeling and symmetry.