The underlying mechanisms for the nucleation of carbon nanotubes as well as their helicity, remain elusive. Here, using van der Waals dispersion force calculations implemented within density functional theory, we study the cap formation, believed to be responsible for the chirality of surface-catalyzed carbon nanotubes. We find the energetics associated with growth along different facets to be independent of the surface orientation and that the growth across an edge along the axis of the metal particle leads to a perfect honeycomb lattice in a curved geometry. The formation of defects in the graphene matrix, which bend the carbon plane, requires that two or more graphene embryos with significantly different growth axis merge. Such scenario is only possible at the front- or back-end of the metal particle where growth symmetry is broken. The graphene embryos reconstruct their hexagonal structure into pentagons, heptagons, and octagons counterpart to accommodate the tube curvature.