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Recent experiments on the Ba3XSb2O9 family have revealed materials that potentially realize spin-and spin-orbital liquid physics. However, the lattice structure of these materials is complicated due to the presence of charged X2+-Sb5+ dumbbells, with two possible orientations. To model the lattice structure, we consider a frustrated model of charged dumbbells on the triangular lattice, with long-range Coulomb interactions. We study this model using Monte Carlo simulation, and find a freezing temperature, T-frz, at which the simulated structure factor matches well to low-temperature x-ray diffraction data for Ba3CuSb2O9. At T = T-frz we find a complicated "branching" structure of superexchange-linked X2+ clusters, which form a fractal pattern with fractal dimension d(f) = 1.90. We show that this gives a natural explanation for the presence of orphan spins. Finally we provide a plausible mechanism by which such dumbbell disorder can promote a spin-orbital resonant state with delocalized orphan spins.