Robustness and generalization are two challenging problems for learning point cloud represen-tation. To tackle these problems, we first design a novel geometry coding model, which can effectively use an invariant eigengraph to group points with similar geometric information, even when such points are far from each other. We also introduce a large-scale point cloud dataset, PCNet184. It consists of 184 categories and 51,915 synthetic objects, which brings new challenges for point cloud classification, and provides a new benchmark to assess point cloud cross-domain generalization. Finally, we perform exten-sive experiments on point cloud classification, using ModelNet40, ScanObjectNN, and our PCNet184, and segmentation, using ShapeNetPart and S3DIS. Our method achieves comparable performance to state-of-the-art methods on these datasets, for both supervised and unsupervised learning. Code and our dataset are available at https://github.com/MingyeXu/PCNet184.