Precision-folded, high strength, fatigue-resistant structures and a sheet therefore are disclosed. To form the structures, methods for precision bending of a sheet of material along a bend line and a sheet of material formed with bending strap-defining structures, such as slits or grooves, are disclosed. Methods include steps of designing and then separately forming longitudinally extending slits or grooves through the sheet of material in axially spaced relation to produce precise bending of the sheet when bent along the bend line. The bending straps have a configuration and orientation which increases their strength and fatigue resistance, and most preferably slits or arcs are used which causes edges to be engaged and supported on faces of the sheet material on opposite sides of the slits or arcs. The edge-to-face contact produces bending along a virtual fulcrum position in superimposed relation to the bend line. Several slit embodiments suitable for producing edge-to-face engagement support and precise bending are disclosed. With these teachings, forming numerous three-dimensional load-bearing structures from a two dimensional sheet are enabled. Examples of straight and curved beams, chassis, and exoskeletons are disclosed.