3D printed custom chromatographic stationary phases are now a reality. Using the Lattice Boltzmann Method, we compare the chromatographic performance of random packing of monodisperse spheres, open tubular columns (OTC) and stationary phases based on three triply periodic minimal surfaces (TPMS): Schwarz Diamond (SD), Schoen Gyroid (SG) and Schwarz Primitive (SP). Three performance metrics were employed in this comparison: i) reduced plate height, ii) Darcy number, iii) kinetic performance factor. Each simulated geometry was unconfined with an impermeable stationary phase to remove wall effects and pore diffusion. The performance was studied for macro- porosities in the range 0.2 to 0.8, depending on the geometry. OTCs were found to have superior permeability to both random sphere packing and TPMS structures across the entire porosity range. At porosity greater than 0.366, the Schwarz Diamond medium achieved the lowest levels of band broadening and greatest kinetic performance. The reduced plate height of all stationary phase geometries was shown to increase with bed porosity. The kinetic performance was found to increase with porosity for TPMS structures, decrease with porosity for random packing and be independent of porosity for OTCs. This work illustrates that chromatographic stationary phase geometries based on TPMS structures are theoretically competitive with random packing and open tubular columns and their feasibility for practical chromatography should continue to be explored.