The paper presents a set stabilizing framework for distributed control design to achieve circular formations for rigid bodies in three-dimensional Euclidean space. Information exchange between the rigid bodies is modeled by a directed graph which is assumed to have a spanning tree. Actuation scenarios of fully actuated, degree-one underactuated, and degree-two underactuated rigid bodies are addressed. Control design is based on a hierarchical approach that relies on a reduction principle for asymptotic stability of closed sets.