Cellular lattices with architectural intricacy or metamaterials have gained a substantial amount of attention in the past decade due to the recent advances in additive manufacturing methods. The lattice topology controls its physical and mechanical properties; therefore, the main challenge is selecting the appropriate lattice topology for a desired function and application. In this work, we comprehensively study the topology–property relationship of three classes of polymer metamaterials based on triply periodic minimal surfaces (TPMS) of sheet/shell and ligament types, and other types of well-known strut-based lattices. The study uses a holistic approach of designing, additive manufacturing, microstructural characterization, and compressive uniaxial mechanical testing of these polymer lattices that are 3D-printed using the laser powder bed fusion technique known as selective laser sintering (SLS). In total, 55 lattices with different topologies and relative densities were 3D-printed and tested. Printing quality was assessed using scanning electron microscopy and micro-computed tomography. The extracted mechanical properties of elastic modulus, yield strength, plateau strength, and energy absorption are thoroughly compared between the different lattice architectures. The results show that all the investigated ligament-based TPMS polymer lattices exhibit bending-dominated elastic and plastic behavior, indicating that they are suitable candidates for energy absorbing applications. The sheet-based TPMS polymer lattices, similarly to the well-known Octet-Truss lattice, exhibited an elastic stretching-dominated mode of deformation and proved to have exceptional stiffness as compared to all other topologies, especially at low relative densities. However, the sheet-based TPMS polymer lattices exhibited a bending-dominated plastic behavior which is mainly driven by manufacturing defects. Overall, however, sheet-based TPMS polymer lattices exhibited the best mechanical properties, followed by strut-based lattices and finally by ligament-based TPMS lattices. Finally, it is depicted that at high relative densities, the mechanical properties of lattices of various architectures tend to converge, which implies that the topological effect is more significant at low relative densities. Generally, this study provides important insights about the selection of polymer mechanical metamaterials for various applications, and shows the superiority of TPMS-based polymer metamaterials as compared to several other classes of polymer mechanical metamaterials. [ABSTRACT FROM AUTHOR]