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C 60 is a model system to study molecule-surface interactions and phase transitions due to its high symmetry and strong covalent π bonding within the molecule versus weak van-der-Waals coupling between neighboring molecules. In the solid, at room temperature, the molecule rotates and behaves as a sphere. However, the pentagonal and hexagonal atomic arrangement imposes deviations from the spherical symmetry that become important at low temperatures. The orientation of the C 60 can be viewed to represent classic spins. For geometrical reasons the preferred orientation of neighboring C 60 cannot be satisfied for all of the neighboring molecules, making C 60 a model for disordered spin systems with frustration. We study several molecular layers of C 60 islands on highly oriented pyrolytic graphite using scanning tunneling microscopy at liquid nitrogen temperatures. By imaging several layers we obtain a limited access to the three-dimensional rotational structure of the molecules in an island. We find one rotationally disordered layer between two partially rotationally ordered layers with hexagonal patterns. This exotic pattern shows an example of the local distribution of order and disorder in geometrically frustrated systems. Scanning tunneling spectroscopy data confirms the weak interactions of neighboring molecules., (Creative Commons Attribution license.)