In four experiments we investigated whether human observers are able to use certain regularities in polygons when they have to indicate which polygon they perceive as the more regular in a paired comparison task. From our results we conclude that regularities that are restricted to the contour do not play a role in judgments of regularity. For instance, equilateral polygons are not considered to be more regular than entirely random polygons. Only bilaterally symmetric polygons are consistently judged as regular. However, we show that this is caused by regularities across the polygon. These results are at odds with approaches that assume that regularities along the contour play an important part in visual perception.