A hexagonal box is formed from a box blank having a rectangular main body divided into six sections which are separated by score lines so that the main body can be folded to create the hexagonal box. The main body has a set of six flaps extending from one end of the six sections, and a second set of six independent flaps extending from the other end of the six sections. Preferably, at least two-thirds of the end-flaps are non-rectangular. Once the box blank is folded into a hexagonal box, the end-flaps may folded inward to create closed ends with minimal end-flap overlap. The hexagonal boxes may be constructed to have handles. A plurality of boxes may be grouped together into a honeycomb formation to maximize the packing density for shipment or transport.