Peirce applied the three categories to derive a typology of hypoicons:
Hypoicons may be roughly divided according to the mode of firstness of which they partake. Those which partake of simple qualities, or first firstnesses, are images; those which represent the relations, mainly dyadic, or so regarded, of the parts of one thing by analogous relations in their own parts, are diagrams; those which represent the representative character of a representamen by representing a parallelism in something else, are metaphors.
Images, characterized as signs of first-firstness, represent simple qualities that partake in iconic semioses when a simple quality from the object is communicated through the mediation of an instantiated sign. The qualities that compose an image possess the same properties as the qualities of the object of the image. It is something perceived immediately. It is indivisible, indecomposable and unstructured. An example of image is an olfactory percept made of properties that can qualitatively distinguish the object of the image itself.
If the sign has the character of second-firstness, then it is not an image, but a diagram. Diagrams signify, through the relations between their parts, the analogous relations between parts of their objects. Whereas an image is related to its object by means of sharing analogous simple qualities, a diagram relates to its object by means of sharing an analogous arrangement of relations. As such, the object of a diagrammatic hypoicon is always an intelligible relation. A typical example of diagrams would be geometrical figures created to demonstrate a theorema. Peirce gives an example about algebra: «in fact, every algebraic equation is an icon, since that shows, through their algebraic signs (which are not themselves icons) relations of the quantities involved».
However if the analogy between sign and object is not held in terms of neither qualities nor relations, but of interpretative effects, then we have a hypoiconic metaphor. Metaphors signify through indirect comparisons between sign and object on the basis of their interpretative effects. In other words, the interpretant of the iconic-metaphorical sign is analogous to the interpretant of its object. As such, they have the character of third-firstness. An example of a metaphor would be the sentence “her flatmate is a pig”. It does not mean that the person’s flatmate is an actual pig (the animal), but that an analogous interpretative effect can be established between the behavior of her flatmate and a pig: they are both dirty, nasty, etc.