Peirce called an icon apart from a label, legend, or other index attached to it, a "hypoicon", and divided the hypoicon into three classes: (a) the "image", which depends on a simple quality; (b) the "diagram", whose internal relations, mainly dyadic or so taken, represent by analogy the relations in something; and (c) the "metaphor", which represents the representative character of a sign by representing a parallelism in something else. A diagram can be geometric, or can consist in an array of algebraic expressions, or even in the common form "All __ is ___" which is subjectable, like any diagram, to logical or mathematical transformations. Peirce held that mathematics is done by diagrammatic thinking — observation of, and experimentation on, diagrams. Peirce developed for deductive logic a system of visual existential graphs, which continue to be researched today.