We have employed the self-consistent charge density-functional tight-binding, the density functional theory and the classical molecular dynamics methods to study new geodesic polyarenes, which can be synthesized via the regiospecific cove-region closure and HF elimination. We show that the shape of new polyarenes may be altered and controlled by the presence of C-60 fullerenes. The high intrinsic curvature of the geodesic arenes facilitates fusion with C-60 fullerenes. This propensity to fuse is consistent with the hypothesis of an optimal value of the bond-puckering angle at which graphene-like structures show maximum reactivity. (C) 2014 Elsevier B.V. All rights reserved.