Abstract The number of inlets of a hexagonal system H is denoted by r ( H ) and defined as the sum of the fissures, bays, coves, and fjords of H . It is well known that the parameter r plays an important role in the theory of molecular descriptors. Let Λ n and Γ m denote the set of hexagonal systems with n vertices and m edges, respectively. In this paper we find sharp lower bounds for the number of inlets on Λ n and Γ m . As a consequence, we determine extremal values of the Randić, harmonic, and geometric‐arithmetic indices over Λ n and Γ m .