The flow regime around a hexagonal polygon with low Reynolds numbers Re < 200 is numerically investigated in two different orientations namely face- and corner oriented. The basic flow characteristics, including drag coefficient, lift coefficient, Strouhal number and critical Reynolds number of the hexagonal cylinders, are calculated by solving the Navier–Stokes and mass conservation (continuity) equations, using the Simple (semi-implicit method for pressure-linked equations) algorithm. Within the studied range of Re, the predicted lift coefficient and Strouhal number of the face-oriented hexagon were higher than those of the corner-oriented hexagon. In contrast, the predicted drag coefficient and critical Reynolds number of the corner-oriented hexagon were greater than those of the face-oriented one. Flow characteristics of a novel textured geometry are also studied using three-dimensional transient analysis. The Strouhal number St of the textured geometry was found to be in between the St of both the hexagonal cylinders, and its lift coefficient is lower than that of the hexagonal cylinders. The computational fluid dynamics results show that, within the studied Reynolds number range, the drag coefficient of the textured pipe is almost equal to that of the circular cylinder while its lift coefficient is substantially smaller than that of circular and face- and corner-oriented hexagon pipes.