Unfoldable

Unfoldable is an English adjective formed from the prefix un- and the word foldable. It is used to describe objects or components that are not designed to be folded, or that resist folding under ordinary forces. The term often appears in contexts involving rigid construction, fixed forms, or permanently extended configurations. In everyday language it contrasts with foldable or collapsible, which describe things intended to be folded for storage or transport.

In geometry and design, unfoldability can refer to the mathematical property of turning a three‑dimensional shape into a single two‑dimensional pattern by cutting along certain lines, known as an unfolding or net. Some polyhedral shapes admit nets that lay flat without overlaps; others do not, depending on the definitions and constraints used in a given study. The concept is studied in fields such as computational geometry, origami mathematics, and industrial design, where the feasibility and limitations of flattening complex structures are of interest.

Etymology and usage notes: unfoldable is formed from un- plus foldable, and has appeared in English usage since the 19th century. While in everyday speech it often describes objects that are not intended to be folded, in technical contexts it relates to the broader question of whether a shape or pattern can be unfolded into a flat form.

See also: foldable, unfold, unfolding, origami, polyhedron, net, collapsible.