Existing representation learning methods of cultural relics require numerous labels. Manual labeling is time-consuming and labor-intensive. Furthermore， supervised learning methods cannot effectively learn the internal structure information of point clouds. We propose an unsupervised representation learning network to extract the deep features of ceramic cultural relics. The approach is based on local-global bidirectional reasoning. First， we propose a multi-scale shell convolution-based hierarchical encoder to extract local features at different scales. Second， the local-to-global reasoning module is used to map the extracted local features to the global features. The differences between the two types of features are measured using metric learning for iterative learning. Third， a fold-based decoder is used to obtain better reconstruction effects from the acquired global features in a coarse-to-fine manner. A local-to-global reasoning module supervises only the local representation to be near the global one. We propose using a low-level generation task as a self-supervision signal. The global feature can capture more basic structural information about point clouds， and the bidirectional inference between local structures and global shapes at different levels was used to learn point cloud representations. Finally， the learned representations are applied in the downstream task of point cloud classification. Experiments on the Terracotta Warriors and ModelNet40 datasets show that the proposed model significantly improves in terms of classification accuracy. The classification accuracies were 93.33% and 92.02%， respectively. The algorithm improved by approximately 4.4% and 2.82% compared with the supervised algorithm PointNet. The results demonstrate that our model achieves a comparable performance and narrows the gap between unsupervised and supervised learning approaches in downstream object classification tasks.