Abstract The search for designing and fabricating truly tissue‐like scaffolds is one of the grand challenges in bone tissue engineering. The question on which parameters are actually the most representative of scaffold architecture and, thus, have to be more carefully designed and considered for assessing the scaffold suitability still remains partially open, but permeability and related microstructural parameters show great promise. In this work, we used vat photopolymerization to fabricate three couples of hydroxyapatite scaffolds with different triply periodic minimal surfaces, that are, diamond, gyroid, and I‐graph and Wrapped Package (IWP), and for the first time experimentally assessed the Darcian intrinsic permeability of such structures by an acoustic method. Furthermore, we determined the major mass transport properties of these scaffolds (pore tortuosity and pore narrowing ratio) from the microtomographic images of the samples.