The word "in-volute" means something that is rolled or curved inwardly. Its antonyms, therefore, would be words that imply a different type of shape or orientation. Some possible antonyms might include "outward," "straight," "linear," "unrolled," or "unfolded." These words would describe objects which do not follow the inwardly curving pattern of an involute shape. In the context of mathematics, another possible antonym might be "evolute" - a shape which is produced when the tangent of a curve is traced. In everyday language, however, the most likely opposite of "in-volute" would simply be a basic shape that is not curled or spiraled in any way.