Abstract: The invention is concerned with the formation of modular units from individual plate-like elements and other elements with special interlocking joints at their ends that allow them to form cubes that can be grouped together to form storage "cubbies" and modular structural systems and toy construction sets and the like, wherein, in one embodiment, the plates are formed with one end having studs on a 45 degree angled surface, and the other end having receptacles or openings such as sockets on a 45 degree angled surface for interlocking with a second mating plate like the first, but in which the studs and sockets are interchanged, allowing a cube to be formed by two of each type of plate, with the use of studs and sockets on the surfaces allowing two or more such cubes to stick together; and wherein, in another embodiment, the cube is made from four identical plates, as by an extrusion process, where one end of a plate contains double male features, such as barb arrows, and the other end contains double correspo