Haptic perception of shape is based on kinesthetic and tactile information synthesized across space and time. We studied this process by having subjects move along the edges of multisided shapes and then remember and reproduce the shapes. With eyes closed, subjects moved a robot manipulandum whose force field was programmed to simulate a quadrilateral boundary in a horizontal plane. When subjects then reproduced the quadrilateral using the same manipulandum, with eyes still closed but now with the force field set to zero, they made consistent errors, overestimating the lengths of short segments and underestimating long ones, as well as overestimating acute angles and underestimating obtuse ones. Consequently their reproductions were more regular than the shapes they had experienced. When subjects felt the same quadrilaterals with the same manipulandum but drew them on a vertical screen with visual feedback, they made similar errors, indicating that their distortions reflected mainly perceptual rather than motor processes. In a third experiment, subjects explored the three sides of an open shape in a fixed order. The results revealed a temporal pattern of interactions, where the lengths and angles of previously-explored segments influenced the drawing of later segments. In all tasks, our subjects were as accurate as subjects in earlier studies who haptically explored only single lines or angles, suggesting that the mental processes that synthesize haptic data from multiple segments into complete shapes do not introduce any net error.