  We model gravitating relativistic 3D spheres composed of an anisotropic fluid
in which the radial and transverse components of the pressure correspond to the
vacuum energy and a generalized polytropic equation-of-state, respectively. By
using the generalized Tolman-Oppenheimer-Volkoff (TOV) equation, and solving
the complete system of equations for these anisotropic generalized polytropic
spheres, for a given range of model parameters, we find three novel classes of
asymptotically AdS black hole solutions with regular core. We show the
regularity of the solutions using curvature scalars and the formalism of
geodesic completeness. Then, using the eigenvalues of the Riemann curvature
tensor, we consider the effects of repulsive gravity in the three static 3D
regular black holes, concluding that their regular behavior can be explained as
due to the presence of repulsive gravity near the center of the objects.
Finally, we study the stability of the regular black holes under the flow of
the energy through the Cauchy horizon.
