Cyclocarbon is a cyclic molecule composed of sp-hybridized carbons connected to each other. Earlier, cyclocarbons have been explored experimentally and there are evidences of their formation in the gas phase, but for a long time, no one can provide direct molecular morphology for them. In 2019, cyclo [18]carbon (C18) was first observed in the condensed phase, ending a long-standing controversy over the structure of this unique carbon allotrope and reigniting a wave of research on it. Over the next three years, scientists synthesized cyclo[n]carbon molecules with various sizes, including n = 6, 10, 12, 13, 14, 16, 20, and 26. Theoretical chemists have also conducted extensive research on the special properties and potential applications of cyclocarbon systems in recent years, among which we have achieved meaningful results in many aspects of C18 and related compounds, including geometric structure, electronic structure, ring strain, aromaticity, optical nonlinearity, intermolecular interaction, external field effect, dynamic behavior, excited state, and so on. Multiple works have speculated or confirmed that the high reactivity of cyclocarbons and their precursors allows them to fuse through covalent coupling, opening up avenues for molecular polymerization into bigger carbon rings. There are also indications that cyclocarbons are valuable precursors for building three-dimensional carbon networks and forming fullerenes in graphite vapor. These statements all imply the possibility of encountering cyclocarbon molecules and other carbon materials in real space. Graphene and C60 fullerene are recognized as two of the most typical carbon materials, which have had a great impact on the development of chemistry and materials. Recently, Chen et al. performed the interaction of C18 with graphene by periodic and non-periodic calculations. The nature of the interaction between C18 and graphene was found to be essentially the same as that between monomers in C18 dimer, but all components of the high order symmetry-adapted perturbation theory (SAPT) in C18-graphene complex are about three times as large as those in C18 dimer, indicating that the intermolecular interaction is much stronger in the former. This conclusion is strictly consistent with our results obtained by high-precision quantum chemical calculations . As of now, however, the complexation behavior of cyclocarbons with C60 fullerene has not been reported.