The ability to perceive the shapes of things as enduring through changes in how they stimulate our sense organs is vital to our sense of stability in the world. But what sort of capacity is shape constancy, and how is it reflected in perceptual experience? This paper defends a pluralist account of shape constancy: There are multiple kinds of shape constancy centered on geometrical properties at various levels of abstraction, and properties at these various levels feature in the content of (...) perceptual experience, governing patterns of apparent shape similarity. I propose that the varieties of shape constancy are subserved by the syntactic complexity of perceptual shape representations. By assigning discrete constituents to various abstract shape parameters, these representations attune us to the preservation of certain abstract shape properties through changes in more determinate shape properties. Finally, I draw broader lessons concerning the nature and function of perceptual constancy. (shrink)