Triply Periodic Minimal Surfaces (TPMS) possess locally minimized surface area under the constraint of periodic boundary conditions. Different families of surfaces were obtained with different topologies satisfying such conditions. Examples of such families include Primitive (P), Gyroid (G) and Diamond (D) surfaces. From a purely mathematical subject, TPMS have been recently found in materials science as optimal geometries for structural applications. Proposed by Mackay and Terrones in 1991, schwarzites are 3D crystalline porous carbon nanocrystals exhibiting a TPMS-like surface topology. Although their complex topology poses serious limitations on their synthesis with conventional nanoscale fabrication methods, such as Chemical Vapour Deposition (CVD), schwarzites can be fabricated by Additive Manufacturing (AM) techniques, such as 3D Printing. In this work, we used an optimized atomic model of a schwarzite structure from the D family (D8bal) to generate a surface mesh that was subsequently used for 3D-printing through Fused Deposition Modelling (FDM). This D schwarzite was 3D-printed with thermoplastic PolyLactic Acid (PLA) polymer filaments. Mechanical properties under uniaxial compression were investigated for both the atomic model and the 3D-printed one. Fully atomistic Molecular Dynamics (MD) simulations were also carried out to investigate the uniaxial compression behavior of the D8bal atomic model. Mechanical testings were performed on the 3D-printed schwarzite where the deformation mechanisms were found to be similar to those observed in MD simulations. These results are suggestive of a scale-independent mechanical behavior that is dominated by structural topology.