Abstract Conceptual spaces are a knowledge representation framework in which concepts are represented geometrically, using convex regions. Motivated by the fact that exact conceptual spaces are usually difficult to obtain, we study the problem of spatial reasoning about qualitative abstractions of such representations. In particular, we consider the problem of deciding whether an RCC8 network extended with constraints about betweenness can be realized using bounded and convex regions in a highdimensional Euclidean space. After showing that this decision problem is PSPACE-hard in general, we introduce an important fragment for which deciding realizability is NP-complete.