The design and construction of non-flat interactive surfaces is an emerging field of research. In this paper, we propose a design space for such displays in order to support structured discussions about differences and design possibilities within this area. Our design space is spanned by basic dimensions of shaped display surfaces, such as size, form and texture. As a starting point, we classify three prototypes from diverse deployment scenarios within it. Based on existing user studies, we discuss possible effects of the respective display categories. At the workshop, we would like to discuss and enhance the design space by integrating further novel non-flat displays, possibly identify additional dimensions and generalizable effects of the different display properties.