The construction of type-II or S-scheme heterojunctions can effectively accelerate the directional migration of charge carriers and inhibit the recombination of electron−hole pairs to improve the catalytic performance of the composite catalyst; therefore, the construction and formation mechanism of a heterojunction are worth further investigation. Herein, Cu 2 O@Cu 4 (SO 4 )-(OH) 6 •H 2 O core−shell polyhedral heterojunctions were fabricated via in situ etching Cu 2 O with octahedral, cuboctahedral, and cubic shapes by sodium thiosulfate (Na 2 S 2 O 3 ). Cu 2 O@Cu 4 (SO 4 )(OH) 6 •H 2 O polyhedral heterojunctions demonstrated obviously enhanced sterilization and degradation performance than the corresponding single Cu 2 O polyhedra and Cu 4 (SO 4 )(OH) 6 •H 2 O. When Cu 2 O with a different morphology contacts with Cu 4 (SO 4 )(OH) 6 •H 2 O, a built-in electric field is established at the interface due to the difference in Fermi level (E f ); meanwhile, the direction of band bending and the band alignment are determined. These lead to the different migration pathways of electrons and holes, and thereby, a type-II or S-scheme heterojunction is constructed. The results showed that octahedral o-Cu 2 O@ Cu 4 (SO 4 )(OH) 6 •H 2 O is an S-scheme heterojunction; however, cuboctahedral co-Cu 2 O@Cu 4 (SO 4 )(OH) 6 •H 2 O and cubic c-Cu 2 O@Cu 4 (SO 4 )(OH) 6 •H 2 O are type-II heterojunctions. By means of X-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), diffuse reflectance spectra (DRS), and Mott−Schottky analyses, the band alignments, Fermi levels, and band offsets (ΔE CB , ΔE VB ) of Cu 2 O@Cu 4 (SO 4 )(OH) 6 •H 2 O polyhedral heterojunctions were estimated; the results indicated that the catalytic ability of the composite catalyst is determined by the type of heterojunction and the sizes of band offsets. Cubic c-Cu 2 O@Cu 4 (SO 4 )(OH) 6 •H 2 O has the strongest driving force (namely, biggest band offsets) to accelerate charge migration and effectively separate charge carriers, so it exhibits the strongest catalytic bactericidal and degrading abilities.