A rotating polygon mirror is commonly used in contemporary printing devices. The understanding of the flow field around the rotating mirror is essential for analysis and design, since reduction of the hydrodynamic load torque directly leads to an improvement in the performance. In this paper, a numerical analysis has been conducted for the flow in the space between a fixed outer cylinder and a rotating octagonal inner cylinder. Discretized transport equations are solved for two-dimensional and three-dimensional time-dependent constant property flows using a second-order accurate finite volume scheme within the context of SIMPLER-based iterative methodology. Two-dimensional calculations show a shear-driven recirculating flow in cavity regions, while three-dimensional calculations reveal a distinct turbulent flow structure. The hydrodynamic loss torque is mainly due to an asymmetric pressure distribution on the polygon surface especially at high rotating speed. This result is qualitatively confirmed by a simple model experiment.