Ever since the discovery of fullerenes, their mono- and multi-functionalization by exohedral addition chemistry has been a fundamental topic. A few years ago, a topochemically controlled regiospecific difunctionalization of C60 fullerene by anthracene in the solid state was discovered. In the present work, we analyse the mechanism of this unique reaction, where an anthracene molecule is transferred from one C60 mono-adduct to another one, under exclusive formation of equal amounts of C60 and of the difficult to make, highly useful, antipodal C60 bis-adduct. 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 undergoing stabilizing interactions with both neighbouring fullerene molecules, facilitating the reaction kinetically. In the intermediate, a planar anthracene molecule is sandwiched between two neighbouring fullerenes and forms equally strong 'double-decker' type π-π stacking interactions with both of these fullerenes. Analysis with the distortion interaction model shows that the anthracene unit of the intermediate is almost planar with minimal distortion. This analysis highlights the existence of simultaneous 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.