This paper is a radical break with a view of multilingualism as an arrangement or hierarchy of different languages which produces more or less visibility for these named varieties. Rather, it takes as its starting point a view of multilingualism as situated within a matrix of social relations, constituted in different times and spaces, between people carrying different histories, attitudes, and feelings. In an attempt to find new ways of representing these social rationalities, we argue for a topological view of multilingualism. This perspective draws attention to the ways in which the diverse facets of multilingualism interconnect and relate in different time-spaces. Our data draw on four artistic visualisations of multilingualism produced by students on a course which sought to explore new ways of re-imagining multilingualism. The posters and artefacts produced on this course stimulated our view of multilingualism as a networked, fluid and mobile typology, or as an n-dimensional form which shifts and changes as it rotates through time and space. We then link this conception to our discussion of Linguistic Citizenship as an n-dimensional topological phenomenon
