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We propose a novel method based on teacher-student learning framework for 3D human pose estimation without any 3D annotation or side information. To solve this unsupervised-learning problem, the teacher network adopts pose-dictionary-based modeling for regularization to estimate a physically plausible 3D pose. To handle the decomposition ambiguity in the teacher network, we propose a cycle-consistent architecture promoting a 3D rotation-invariant property to train the teacher network. To further improve the estimation accuracy, the student network adopts a novel graph convolution network for flexibility to directly estimate the 3D coordinates. Another cycle-consistent architecture promoting 3D rotation-equivariant property is adopted to exploit geometry consistency, together with knowledge distillation from the teacher network to improve the pose estimation performance. We conduct extensive experiments on Human3.6M and MPI-INF-3DHP. Our method reduces the 3D joint prediction error by 11.4% compared to state-of-the-art unsupervised methods and also outperforms many weakly-supervised methods that use side information on Human3.6M. Code will be available at https://github.com/sjtuxcx/ITES.