This paper addresses the generality problem arising for the use of spatial figures in geometry by emphasizing Kant’s notion of the schema of a geometrical concept (in contrast to an individual figure falling under that concept). It then relates this notion of schema to space as a form of intuition by connecting geometrical constructions (examples of Kantian schemata) with the possible perspectives of the perceiving subject within space as the form of outer intuition. And it uses this relationship between geometrical schemata and what I thus call "perceptual space" (the form of outer intuition) to develop a new interpretation of the relationship between the understanding and sensibility in section 26 of the Transcendental Deduction. The result is a reading of Kant on space and geometry that shows how geometrical, perceptual, and physical space are necessarily related to one another.