An investigation into the efficiency of two-dimensional polygonal structures undergoing transverse vortex-induced-vibration (VIV) is presented. The study aims at enhancing the yield in high oscillation amplitude for effective energy harvesting, for elements with a mass ratio of ≈25, subjected to laminar cross-flow at Reynolds number of ≈150. The efficiency of an isotoxal-star element with octagonal geometry is numerically investigated and compared to canonical circular cylinders. Under static conditions, the isotoxal-star element yields higher magnitude of fluctuating transverse force compared to the circular cylinders. When undergoing VIV at zero structural damping, the two cylinders have almost identical maximum oscillation amplitude despite the difference in the vortex strength and transverse force. Further investigations using an isotoxal-star element with diamond geometry and a triangular element suggests that VIV amplitude at zero structural damping is predominately governed by the magnitude of transverse drag force of the cross-section. At a structural damping ratio of 0.10, VIV enhancement due to changes in cross-sectional geometry becomes more apparent. Results suggest that VIV amplitude under damped condition is dependent on both the magnitude of fluctuating transverse force and the magnitude of transverse drag force. The two forces play different roles with regards to VIV response: a higher magnitude of fluctuating transverse force from a stronger von Karman vortex trail fosters the initiation of VIV. Conversely, strong transverse drag originating from the strong vorticity generated during transverse motions reduces the VIV. As such, VIV enhancement is a consequence of streamwise velocity or crossflow, while conversely, its reduction is primarily attributed to stronger transverse velocities. Results therefore suggest that enhanced VIV response could be potentially obtained through tailoring of the cross-sectional area to yield increased fluctuating transverse force while minimising transverse drag, represented here by the triangular element. Yet the compromise with regards to maintaining an effective omnidirectional performance of the elements renders isotoxal-star structures with multiple vertices (hereby assumed octagonal) more suitable for practical energy harvesting applications.