A building in which a core is attached to a ground floor foundation slab; a roof is attached to the upper end of the core; floors of any desired planar shape are attached to the core at the appropriate heights, intermediate the roof and the ground floor foundation slab; and wall panels are attached between the roof and the ground floor foundation slab around the periphery of the building. Also, the floors and roof are attached to the wall panels. The core is preferably as claimed and described in U.S. patent application Ser. No. 12/748,751 and may be attached to one side of the ground floor foundation slab. The floors may extend the entire length and/or width of the building or only a portion of the length and/or width. If they do not extend the entire length and/or width of the building, the free ends of the floors are supported by a cross beam that attaches to the walls on either side or a support wall or beam that extends to the floor below or the ground floor slab, or any other suitable method for support.