  We study the motion of a single point vortex in simply and multiply connected
polygonal domains. In case of multiply connected domains, the polygonal
obstacles can be viewed as the cross-sections of 3D polygonal cylinders. First,
we utilize conformal mappings to transfer the polygonal domains onto circular
domains. Then, we employ the Schottky-Klein prime function to compute the
Hamiltonian governing the point vortex motion in circular domains. We compare
between the topological structures of the contour lines of the Hamiltonian in
symmetric and asymmetric domains. Special attention is paid to the interaction
of point vortex trajectories with the polygonal obstacles. In this context, we
discuss the effect of symmetry breaking, and obstacle location and shape on the
behavior of vortex motion.
