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People live in a 3D world. However, existing works on person re-identification (re-id) mostly consider the semantic representation learning in a 2D space, intrinsically limiting the understanding of people. In this work, we address this limitation by exploring the prior knowledge of the 3D body structure. Specifically, we project 2D images to a 3D space and introduce a novel parameter-efficient Omni-scale Graph Network (OG-Net) to learn the pedestrian representation directly from 3D point clouds. OG-Net effectively exploits the local information provided by sparse 3D points and takes advantage of the structure and appearance information in a coherent manner. With the help of 3D geometry information, we can learn a new type of deep re-id feature free from noisy variants, such as scale and viewpoint. To our knowledge, we are among the first attempts to conduct person re-identification in the 3D space. We demonstrate through extensive experiments that the proposed method (1) eases the matching difficulty in the traditional 2D space, (2) exploits the complementary information of 2D appearance and 3D structure, (3) achieves competitive results with limited parameters on four large-scale person re-id datasets, and (4) has good scalability to unseen datasets. Our code, models and generated 3D human data are publicly available at https://github.com/layumi/person-reid-3d .