Abstract: Sheet material building components or units in the shape of different regular polygons of equal edge length have strips of hook-and-pile fastening materials permanently secured so as to extend along their side edges. Hook type fastening material is disposed toward one end portion of each side edge and pile type fastening material is disposed toward the other end portion of each side edge. The strips of hook type and pile type fastening materials alternate around the circumference of each unit. Different units can be connected substantially edge-to-edge by simply placing the desired edges in contact to form a wide variety of two-dimensional or three-dimensional arrays or shapes.