Stratified enumeration of convex benzenoids

In this paper we study an interesting family of benzenoids, the convex benzenoids, introduced in 2012 by Cruz, Gutman and Rada. We give several definitions of convex benzenoids and prove their equivalence. We use the partition of convex benzenoids into the 7 families of shapes: benzene, linear, triangular, trapezoidal, rhomboidal, pentagonal and hexagonal as a basis for an independent stratification and extension of the convex benzenoid enumeration by Reynolds from up to 250 hexagons presented in the OEIS as sequence A116513 to 40 000 hexagons.