We characterize the models of Asher and Vieu’s first-order mereotopology RT0 in terms of mathematical structures with well-defined properties: topological spaces, lattices, and graphs. We give a full representation theorem for the models of the subtheory RT‒ (RT0 without existential axioms) as p-ortholattices (pseudocomplemented, orthocomplemented). We further prove that the finite models of RT‒EC, an extension of RT‒, are isomorphic to a graph representation of portholattices extended by additional edges and we show how to construct finite models of the full mereotopology. The results are compared to representations of Clarke’s mereotopology and known models of the Region Connection Calculus (RCC). Although soundness and completeness of the theory RT0 has been proved with respect to a topological translation of the axioms, our characterization provides more insight into the structural properties of the mereotopological models.