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We study mechanically stable packings of deformable and rigid 2D circulo-polygons using computer simulations. A 2D circulo-polygon is a particle shape formed by the collection of all points equidistant from the edge of a polygon. It is a generalization of the 2D circulo-cylinder and a circle, which are the collections of all points equidistance from a line and a point, respectively. In our model, the circulo-polygon can be deformable, where the only constraint on the particle is that shape factor, the ratio of the area of the polygon to the square of the perimeter, is fixed.