We analyze the mechanism of the topochemically controlled difunctionalization of C60 and anthracene, where an anthracene molecule is transferred from one C60 monoadduct to another one under exclusive formation of equal amounts of C60 and the difficult to make antipodal C60 bisadduct. Our herein disclosed dispersion corrected DFT studies show the anthracene transfer to take place in a synchronous retro Diels-Alder/Diels-Alder reaction: an anthracene molecule dissociates from one fullerene under formation of an intermediate, while already undergoing stabilizing interactions with both neighboring fullerenes, facilitating the reaction kinetically. In the intermediate, a planar anthracene molecule is sandwiched between two neighboring fullerenes and forms equally strong "double-decker" type pi-pi stacking interactions with both of these fullerenes. Analysis with the distorsion interaction model shows that the anthracene unit of the intermediate is almost planar with minimal distorsions. This analysis sheds light on the existence of noncovalent interactions engaging both faces of a planar polyunsaturated ring and two convex fullerene surfaces in an unprecedented 'inverted sandwich' structure. Hence, it sheds light on new strategies to design functional fullerene based materials.<br>