We have constructed realistic, self-consistent models of triaxial elliptical galaxies embedded in triaxial dark matter halos. Self-consistent solutions by means of the standard orbital superposition technique introduced by Schwarzschild were found in each of the three cases studied. Chaotic orbits were found to be important in all of the models, and their presence was shown to imply a possible slow evolution of the shapes of the halos. The equilibrium velocity distribution is reproduced by a Lorentzian function better than by a Gaussian. Our results demonstrate for the first time that triaxial dark matter halos can co-exist with triaxial galaxies.
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