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The high symmetry and round shape of the fullerene molecules induce orientational phenomena that play an important role in the properties of the fullerene compounds. This is illustrated in this review which is focused on the orientational properties of C60 monomer and polymer structures. First, the orientational state of C60 at room temperature, its peculiar orientational ordering phase transition and the associated glassy state are described, together with the corresponding temperature-pressure phase diagram. Then, a summary of the polymerization processes and of the varied structures obtained under high-pressure high-temperature conditions or via doping by alkali metals is proposed. Finally, some information is given on the orientational properties of C60 layers and surfaces.

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