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Qualitative spatial reasoning is often considered to be akin to human reasoning. This, however, is mostly based on the intuition of researchers rather than on empirical data. In this paper we continue our effort in empirically studying the cognitive adequacy of systems of topological relations. As compared to our previous empirical investigation [7], we partially lifted constraints on the shape of regions in configurations that we presented subjects in a grouping task.With a high level of agreement, subjects distinguished between different possibilities of how spatial regions can touch each other. Based on the results of our investigation, we propose to develop a new system of topological relations on a finer level of granularity than previously considered.