We have used atomic force microscopy to study in detail the shape of InAs quantum dots (QDs) grown on GaAs (001) substrates. The QDs are fabricated by partial capping and a subsequent annealing process at low temperature. We observe circular, non-elongated QDs, with rim structures on top. The majority of the QDs located on a step edge have an anisotropic rim structure with a crescent shape, whereas approximately 50% of QDs located on terraces have isotropic rim structures with a ring shape. These results indicate that the rims of non-elongated QDs are not always isotropic, and the formation of an isotropic or anisotropic rim structure is dependent on the location of the QD. (c) 2013 Elsevier B.V. All rights reserved.