A global optimization strategy is applied to Lennard-Jones models describing the stable trapping sites of a dimer in the face-centered cubic Ar-like lattice. Effective volumes of the trapping sites, quantified as the number of host atoms dislodged from the lattice, are mapped onto the parameter space defined by the strength and range of the dimer interaction potentials. The two models considered differ in the host-guest interaction and give very different maps that reflect the effect of local lattice relaxation. A hierarchical complete-linkage clustering technique is applied to identify generic structural types of the dimer accommodations. The dominant types found and enlisted maintain the symmetry of the isolated dimer and possess high tetrahedral and octahedral symmetry of the host environment with respect to the dimer atoms or center and can be roughly classified as the "whole" or "per atom" dimer accommodations. The results are compared to the analysis of the analogous model for trapped atoms and realistic model for trapped alkaline-earth metal dimers. Implications for matrix isolation spectroscopy are discussed.