Learning 3D representations of point clouds that generalize well to arbitrary orientations is a challenge of practical importance in domains ranging from computer vision to molecular modeling. The proposed approach uses a concentric spherical spatial representation, formed by nesting spheres discretized the icosahedral grid, as the basis for structured learning over point clouds. We propose rotationally equivariant convolutions for learning over the concentric spherical grid, which are incorporated into a novel architecture for representation learning that is robust to general rotations in 3D. We demonstrate the effectiveness and extensibility of our approach to problems in different domains, such as 3D shape recognition and predicting fundamental properties of molecular systems.