PolyCubes provide compact representations for closed complex shapes and are essential to many computer graphics applications.Existing automatic PolyCube construction methods usually suffer from poor quality or time-consuming computation. In thispaper, we provide a highly efficient method to compute volumetric PolyCube-maps. Given an input tetrahedral mesh, we utilizetwo novel normal-driven volumetric deformation schemes and a polycube-allowable mesh segmentation to drive the input to avolumetric PolyCube structure. Our method can robustly generate foldover-free and low-distortion PolyCube-maps in practice,and provide a flexible control on the number of corners of Polycubes. Compared with state-of-the-art methods, our method is atleast one order of magnitude faster and has better mapping qualities. We demonstrate the efficiency and efficacy of our method inPolyCube construction and all-hexahedral meshing on various complex models