Abstract: A notched 2D shape may encode information. For instance, a physical tag may display, form or include a polygon that is modified by notches and by one or more holes. This notched 2D shape may encode data that identifies, or provides information regarding, a physical product to which the tag is physically attached. Alternatively, this notched 2D shape may encode any other type of information, such as information about what we sometimes call a product shape or shape matrix. The notched shape may be an octagon that is modified by notches and by one or more holes.