Chiasmus fundamentally involves iconicity. As a bi-lateral symmetrical figure that can have both an ornamental and a rhetorical function, it occurs on all levels of texts - sounds and graphemes, words, sentences, lines, chapters and entire books as well as on the narrative and on the conceptual level. The chiastic mirror-image design in which the second part is balanced against the first is however not limited to language but also appears in art and architecture. As recent cognitive research has shown, chiasmus forms an important strategy through its simple but unique design. This has to do with its spatial shape and how the crisscrossing of lines and paths that takes place in the X-figure is cognized, perceptually and experientially – suggesting itself as the origin of human abilities such as forming analogies and using conceptual integration. This is what my contribution explores, with example from James Joyce’s Ulysses.