Point cloud completion refers to inferring the complete and visually plausible shape from a partial input. Existing point cloud completion methods focus on recovering the global integrity of partial point clouds but lack local structural details. Furthermore, they seldom consider the shape faithfulness of completed results, that some completed points fail to fall into the ground truth position faithfully. To meet the above challenges, we present a multidimensional graph interactional network for progressive point cloud completion. Specifically, we propose a multiresolution multidimensional graph encoder (MRMD GE) to capture the information from both within dimension and cross dimension interactions for the purpose of enhancing the perception of local geometry. Inspired by the FPN, we develop a recursive point cloud pyramid decoder (RPPD) for generating multistage completed point clouds progressively, which incorporates extra feedback connections into the bottom up backbone layers. In addition, we design a depth map discriminator combined with differentiable rendering to match the distribution of generated and real point clouds, making the completed point clouds more faithful to the ground truth. Quantitative and qualitative experiments on Completion3D, Shapenet Part, and KITTI datasets demonstrate that our proposed method has compelling advantages over the state of the art methods.