The self-assembly of the C38H14-bucky-bowl, a fragment bowl of the C-70 fullerene, has been studied with scanning tunneling microscopy on the Cu(111) surface. Isolated molecules adsorb bowl opening-up with the center C6 ring parallel to the surface. In extended 2D islands, however, 1/3 of the molecules are oriented such that the bowl opening points down. From a detailed analysis of relative orientation of the molecules, the nature of intermolecular lateral interactions is identified. In densely packed islands, pi-pi bonding between convex sides of the bowls dominate, while pi-H bonding between rim and convex sides plays the important role in small molecular 2D clusters.