Let k be a local field. To SLn(k) one classically associates a space called a Bruhat-Tits buildings. However, there are also Euclidean buildings which are not associated to such a group, which we call exotic. Some of them still possess lattices, which were recently proved to be non-linear, and are conjectured to be virtually simple. The goal of this project would be to start a geometric study of quotients of buildings, with an emphasis on exotic ones.