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The understanding of the domain wall (DW) dynamics along magnetic nanowires is crucial for spintronic applications. In this work, we perform a detailed analysis of the transverse DW motion along nanowires with polygonal cross-sections. If the DW displaces under a magnetic field above the Walker limit, the oscillatory motion of the DW is observed. The amplitude, the frequency of oscillations, and the DW velocity depend on the number of sides of the nanowire cross-section, being the DW velocity in a wire with a triangular cross-section one order of magnitude larger than that in a circular nanowire. The decrease in the nanowire cross-section area yields a DW behavior similar to the one presented in a cylindrical nanowire, which is explained using an analytical model based on the general kinetic momentum theorem. Micromagnetic simulations reveal that the oscillatory behavior of the DW comes from energy changes due to deformations of the DW shape during the rotation around the nanowire.