Advances in manufacturing technologies have led to the development of a new approach to material selection, in which architectured designs can be created to achieve a specific mechanical objective. Cellular lattice structures have been at the forefront of this movement due to the ability to tailor their mechanical response through tuning of the topology, surface thickness, cell size, and cell density. In this work, the mechanical properties of additively manufactured periodic cellular lattices are evaluated and compared, primarily through the topology and surface thickness parameters. The evaluated lattices were based upon triply periodic minimal surfaces (TPMS), including novel variations on the base TPMS designs, which have not been tested previously. These lattices were fabricated out of Inconel 718 (IN718) through the selective laser melting (SLM) process. Specimens were tested under uniaxial compression, and the resultant mechanical properties were determined. Further discussion of the fabrication quality and deformation behavior of the lattices is provided. Results of this work indicate that the Diamond TPMS lattice has superior mechanical properties to the other lattices tested. Additionally, with the exception of the primitive TPMS lattice, the base TPMS designs exhibited superior mechanical performance to their derivative lattice designs.