The modular design of planar phased array antennas with hexagonal apertures is addressed by means of innovative diamond-shaped tiling techniques. Both tiling configuration and subarray coefficients are optimized to fit user-defined power-mask constraints on the radiation pattern. Toward this end, suitable surface-tiling mathematical theorems are customized to the problem at hand to guarantee optimal performance in case of low/medium-size arrays, while the computationally hard tiling of large arrays is yielded thanks to an effective integer-coded GA-based exploration of the arising high-cardinality solution spaces. By considering ideal as well as real array models, a set of representative benchmark problems is dealt with to assess the effectiveness of the proposed architectures and tiling strategies. Moreover, comparisons with alternative tiling architectures are also performed to show to the interested readers the advantages and the potentialities of the diamond subarraying of hexagonal apertures.