Given a discrete group of isometries of a real hyperbolic space, we can look at its limit set, i.e., the set of accumulation points of its orbits on the sphere at infinity. This is a compact metric space on which the group acts, and which enjoys many interesting geometric, topological, and dynamical features. For example, classical Kleinian groups provide many examples with limit sets that are quasicircles, Cantor sets, and Sierpinski carpets. In this talk, I will discuss how to construct examples whose limit sets are various low-dimensional trees of manifolds. In particular, we answer a question of M. Kapovich, by constructing convex cocompact groups of isometries of real hyperbolic spaces, whose limit sets are Čech cohomology 3-spheres not homeomorphic to S^3. These groups are right-angled Coxeter groups and our construction is flexible enough to produce infinitely many quasi-isometry classes. This is joint work with S. Douba, G.-S. Lee, and L. Marquis.