Geometric fidelity of 3D printed products is critical for additive manufacturing (AM) to be a direct manufacturing technology. Shape deviations of AM built products can be attributed to multiple variation sources such as substrate geometry defect, disturbance in process variables, and material phase change. Three strategies have been reported to improve geometric quality in AM: (1) control process variables x based on the observed disturbance of process variables Δx, (2) control process variables x based on the observed product deviation Δy, and (3) control input product geometry y based on the observed product deviation Δy. This study adopts the third strategy which changes the computer-aided design (CAD) design by optimally compensating the product deviations. To accomplish the goal, a predictive model is desirable to forecast the quality of a wide class of product shapes, particularly considering the vast library of AM built products with complex geometry. Built upon our previous optimal compensation study of cylindrical products, this work aims at a novel statistical predictive modeling and compensation approach to predict and improve the quality of both cylindrical and prismatic parts. Experimental investigation and validation of polyhedrons a indicates the promise of predicting and compensating a wide class of products built through 3D printing technology.