Insulator-based (electrodeless) dielectrophoresis (iDEP) is a promising particle manipulation technique, based on movement of matter in inhomogeneous fields. The inhomogeneity of the field arises because the excitatory field distorts at obstacles (posts). This effect is caused by accumulation of polarization charges at material interfaces. In this study, we utilize a multipole expansion method to investigate the influence of geometry and material on field distortion of posts with arbitrary cross-sections in homogeneous electric fields applied perpendicular to the longitudinal axis of the post. The post then develops a multipole parallel or anti parallel to the excitatory field. The multipoles intensity is defined by the post's structure and material properties and directly influences the DEP particle trapping potential. We analyzed posts with circular and rhombus-shaped cross-sections with different cross-sectional width-to-height ratios and permittivities for their polarization intensity, multipole position, and their particle trapping behavior. A trade-off between high maximum field gradient and high coverage range of the gradient is presented, which is determined by the sharpness of the post's edges. We contribute to the overall understanding of the post polarization mechanism and expect that the results presented will help optimizing the structure of microchannels with arrays of posts for electrodeless DEP application.