A net layer (32) defines the shell (40) of a building, carried by any necessary supports. A hardening layer (34) is applied to fix the shape of the net layer (32) and to establish wall, roof, and floor. Optionally the shell is of sufficient strength to receive application of further layers in order to define an exoskeleton. Structures of roof sections include parallel-sided segments and converging-sided segments, with troughed or domed section shapes. Structures of walls include opposed shell sides (35), (78) and central filler layers (70), together defining an exoskeleton. Posts (72) can add additional structural capacities for supporting walls, roof and floor and can be formed integrally of net (32) and hardener (34).