ABSTRACT. Topological logics are formalisms for reasoning about topological relations between regions. In this paper, we introduce a new inference problem for topological logics, the unifiability problem, which extends the validity problem by allowing one to replace variables by terms before testing for validity. Our main result is that, within the context of the mereotopology of all regular closed polygons of the real plane, unifiable formulas always have finite complete sets of unifiers.