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We report coarse-grained Langevin dynamics simulations of homogeneous mixtures of lobed colloidal particles with opposite charges. We show that dumbbell, trigonal planar, tetrahedral, square planar, trigonal bipyramidal, and octahedral shaped particles form distinct self-assemblies including chains, sheets, crystalline, and spherical structures. The dumbbell and square planar particles predominantly form chains and sheets while other particles form network-like self-assembled morphologies. At higher temperatures and lower charges, non-planar particles form three-dimensional aggregates. We further report on packing arrangements of particles which lead to differences in porosities within self-assembled morphologies. Our results show that the trigonal planar particles form larger porous structures. The self-assembled structures that we report are potentially useful in designing porous biomaterials for biomedical applications.