Direct ink writing is a promising technology for the fabrication of personalized bone grafts, as it enables the customization of their geometrical conformation with high reproducibility and is compatible with the use of self-setting calcium deficient hydroxyapatite inks. However, the scaffolds obtained by DIW consist mostly of convex filaments, which is a limitation since concave surfaces have been shown to promote bone regeneration in vivo. In this work, we explore the use of triply periodic minimal surface (TPMS) designs in DIW of calcium phosphate self-hardening inks as a strategy to obtain scaffolds with controlled concave macropores. The limitations of the printing parameters with high ceramic loaded inks used in DIW enabled achieving only 20% nominal porosities of Gyroid-, Diamond- and Schwarz-based structures. The inherent layered pores from TPMS geometries allowed obtaining concavities typically unattainable via DIW, bearing substantial implications for subsequent osteoinductive capabilities. Although the mechanical properties were lower in the TPMS-based scaffolds than in the orthogonal patterned ones, the blood permeability of the TPMS-based structures was higher. The concave pore architecture enhanced the osteogenic potential of the biomimetic ceramic, increasing SaOs-2 cell adhesion, proliferation, differentiation and mineralisation.