Diffraction of orbital angular momentum carrying Laguerre-Gauss vortex (LGV) beams by N-fold rotationally symmetric regular polygons is studied analytically and experimentally. The structure, symmetry, and dependence of the diffraction pattern on the angular momentum index of the LGV beam and the number of sides in the polygon are systematically investigated and novel features and trends are identified. The evolution of the diffraction pattern and its symmetry with the aperture position relative to the waist was also studied leading to a generalized Friedel's Law for diffraction of LGV beams. PACS numbers:

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