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In recent years, the triply periodic minimal surface (TPMS) has emerged as a new method for producing open cell porous scaffolds because of the superior properties, such as the high surface-to-volume ratio, the zero curvature, etc. On the other hand, the additive manufacturing (AM) technique has made feasible the design and development of TPMS scaffolds with complex microstructures. However, neither the discrepancy between the theoretically designed and the additively manufactured TPMS scaffolds nor the underlying mechanisms is clear so far. The aims of the present study were to quantify the discrepancies between the theoretically designed and the AM produced TPMS scaffolds and to reveal the underlying mechanisms, e.g., the effect of building orientation on the discrepancy. 24 Gyroid scaffolds were produced along the height and width directions of the scaffold using the selective laser melting (SLM) technique (i.e., 12 scaffolds produced in each direction). The discrepancies in the geometric and mechanical properties of the TPMS scaffolds were quantified. Regarding the geometric properties, the discrepancies in the porosity, the dimension and the three-dimensional (3D) geometry of the scaffolds were quantified. Regarding the mechanical properties, the discrepancies in the effective compressive modulus of the scaffolds were evaluated. It is revealed that the porosity in the AM produced scaffold is approximately 12% lower than the designed value. There are approximately 68.1 ± 8.6% added materials in the AM produced scaffolds and the added materials are mostly distributed in the places opposite to the building orientation. The building orientation has no effect on the discrepancy in the scaffold porosity and no effect on the distribution of the added materials (p > 0.05). Regarding the mechanical properties, the compressive moduli of the scaffolds are 24.4% (produced along the height direction) and 14.6% (produced along the width direction) lower than the designed value and are 49.1% and 43.6% lower than the µFE counterparts, indicating that the imperfect bonding and the partially melted powders have a large contribution to the discrepancy in the compressive modulus of the scaffolds. The findings in the present study provide important information for the design and additive manufacturing of TPMS scaffolds.