We consider the expressive power of the first-order structure 〈Ω, C〉 where Ω is either of two of different domains of extended regions in Euclidean space, and C(x,y) is the topological relation “Region x is in contact with region y.” We prove two main theorems: • Let P[Q] be the domain of bounded, non-empty, rational polyhedra in twoor threedimensional Euclidean space. A relation Γ over P[Q] is...