The self-assembly of a hexagonal cylinder-forming diblock copolymer melt under the hexagonal confinement provides a useful method for the fabrication of defect-free hexagonal patterns. However, the validity of this method depends on the commensurability of the hexagonal size to the domain spacing. Here we turn to another lateral confinement whose shape adapts to the hexagonal lattice, i.e. the regular triangle. First, we attempted to verify that the perfect hexagonal patterns are exclusively the thermodynamic stable morphologies in the triangles with whatever sizes using the self-consistent field theory (SCFT). Then, we simulate the annealing kinetics of the confined melt using the SCFT iteration process. We find that a small number of defects are usually formed in a large triangle even with a commensurate size to the domain spacing. Finally, we propose a multi-step annealing process, where the perfect hexagonal patterns are yielded via a heterogenous nucleation process. Importantly, the achievement of the perfect hexagonal patterns does not exhibit a size-incommensurability issue with the triangles, and thus could become a promising nanolithography scheme.