Columnar polymers and liquid crystals obtained from π-conjugated cone-shaped molecules are receiving increasing interest due to the possibility of obtaining unconventional polar organizations that show anisotropic charge transport and unique chiroptical properties. However, and in contrast to the more common planar discotics, the self-assembly of conic or pyramidic molecules in solution remains largely unexplored. Here, we show how a molecular geometry change, from flat to conic, can generate supramolecular landscapes where different self-assembled species, each of them being under thermodynamic equilibrium with the monomer, exist exclusively within distinct regimes. In particular, depending on the solvent nature-aromatic or aliphatic-cone-shaped C3-symmetric subphthalocyanine 1 can undergo self-assembly either as a tail-to-tail dimer, showing monomer-dimer sigmoidal transitions, or as a head-to-tail noncentrosymmetric columnar polymer, exhibiting a nucleation-elongation polymerization mechanism. Moreover, the experimental and theoretical comparison between racemic and enantiopure samples revealed that the two enantiomers (1M and 1P) tend to narcissistically self-sort in the dimer regime, each enantiomer showing a strong preference to associate with itself, but socially self-sort in the polymer regime, favoring an alternate stacking order along the columns.