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Magneto-optical imaging has been used to study vortex penetration into regular polygon-shaped Bi2Sr2CaCu2O8+delta platelets with various geometries (disks, pentagons, squares, and triangles) but known fixed areas. In all cases we observe an exponential dependence of the field of first penetration, H-p, on temperature, consistent with a dominant Bean-Livingston barrier for pancake vortices at our measurement temperatures (45-80K). However, the penetration field consistently decreases with decreasing degree of sample symmetry, in stark contrast to conventional estimates of demagnetization factors using equivalent ellipsoids based on inscribed circles, which predict the reverse trend. Surprisingly, this observation does not appear to have been reported in the literature before. We demonstrate empirically that estimates using equivalent ellipsoids based on circumscribed circles predict the correct qualitative experimental trend in H-p. Our work has important implications for the estimation of appropriate effective demagnetization factors for flux penetration into arbitrarily shaped superconducting bodies.