X-ray computed tomography was applied in imaging 3D printed gyroids used for bioseparation in order to visualize and characterize structures from the entire geometry down to individual nanopores. Methacrylate prints were fabricated with feature sizes of 500 µm, 300 µm and 200 µm, with the material phase exhibiting a porous substructure in all cases. Two X-ray scanners achieved pixel sizes from 5 µm to 16 nm to produce digital representations of samples across multiple length scales as the basis for geometric analysis and flow simulation. At the gyroid scale, imaged samples were visually compared to the original computed aided designs to analyze printing fidelity across all feature sizes. An individual 500 µm feature, part of the overall gyroid structure, was compared and overlaid between the design and imaged volumes where individual printed layers could be identified. Internal subvolumes of all feature sizes were segmented into material and void phases for permeable flow analysis. Small pieces of 3D printed material were optimized for nanotomographic imaging at a pixel size of 63 nm, with all three gyroid samples exhibiting similar geometric characteristics when measured. An average porosity of 45% was obtained that was within the expected design range and a tortuosity factor of 2.52 was measured. Applying a voidage network map enabled the size, location and connectivity of individual pores to be identified, obtaining an average internal pore size of 793 nm. Using the Avizo XLAB plugin at a bulk diffusivity of 7.00 x10 ^-11 m ²s ^-1 resulted in a simulated material diffusivity of 2.17 x10 ^-11 m ²s ^-1 ± 0.16 x10 ^-11 m ²s ^-1.