The Buckminster fullerene C₆₀ molecule was analyzed from the point of view of global and local reactivity. In particular, the dual descriptor--a local reactivity descriptor derived from conceptual density functional theory--was used to describe local reactivity in this molecule. One of the main advantages of using such a descriptor is the simplicity of obtaining accurate information about the local reactivity required to form covalent bonds without needing to perform calculations at higher levels of theory. The descriptor was adapted to the correct symmetry of this molecule in equilibrium so that the isosurface belongs to the totally symmetrical irreducible representation of the respective group of symmetry. Unlike global and some other local reactivity descriptors, correlation effects and basis sets are not critically important when using the dual descriptor because local reactivity is conserved at a qualitative level.