Fivefold symmetry is incompatible with the translational order in all 17 plane groups and is therefore of fundamental interest for two dimensional crystallization processes. A model study on single crystal surfaces, e.g. Cu(111), has been carried out to better understand the fundamental principles of intermolecular interactions between fivefold symmetric corannulene and its derivatives in two-dimensional clusters and lattices, including those consisting of fivefold bowl-shaped (buckybowl) molecules. Rational molecular design and state of the art surface science methods, e.g. Scanning Tunneling Microscopy, Low Energy Electron Diffraction, X-Ray Photoelectron Spectroscopy, Ultraviolet Photoelectron Spectroscopy, Temperature Programmed Desorption, and Reflection Adsorption Infrared Spectroscopy were applied. Several reversible surface phases were identified, including stripes, zig-zag, rosette and rotator phases. The packings of fivefold symmetric molecules was found to exhibit the same patterns upon adsorption as identified in the closest packings of hard pentagons and five-pointed stars.