Spherical particles are widely considered as the benchmark stationary phase for preparative and analytical chromatography. Although this has proven true for randomly packed beds in the past, we challenge this paradigm for ordered packings, the fabrication of which are now feasible through additive manufacturing (3D printing). Using computational fluid dynamics (Lattice Boltzmann Method) this work shows that nonspherical particles can both reduce mobile-phase band broadening and increase permeability compared with spheres in ordered packed beds. In practice, ordered packed beds can only remain physically stable if the particles are fused to form a contiguous matrix, thus creating a positional overlap at the points of fusion between what would otherwise be discrete particles. Overlap is shown to decrease performance of ordered packed beds in all observed cases, thus we recommend it should be kept to the minimum extent necessary to ensure physical stability. Finally, we introduce a metric to estimate column performance, the mean deviated velocity, a quantitative description of the spread of the velocity field in the column. This metric appears to be a good indicator of mobile-phase dispersion in ordered packed bed media, including overlapped beds, and is a useful tool for screening new stationary-phase morphologies without having to perform computationally expensive simulations.