The collective behavior of vibrated hexagonal disks confined in a monolayer is investigated experimentally. Due to the broken circular symmetry, hexagons prefer to rotate upon sufficiently strong driving. Due to the formation of liquid bridges, short-ranged cohesive interactions are introduced upon wetting. Consequently, a nonequilibrium stationary state with the rotating disks self-organized in a hexagonal structure arises. The bond length of the hexagonal structure is slightly smaller than the circumdiameter of a hexagon, indicating geometric frustration. This investigation provides an example where the collective behavior of granular matter is tuned by the shape of individual particles.