Objects with large base areas become ungraspable when they exceed the end-effector's maximum aperture. Existing approaches address this limitation through extrinsic dexterity, which exploits environmental features for non-prehensile manipulation. While grippers have shown some success in this domain, dexterous hands offer superior flexibility and manipulation capabilities that enable richer environmental interactions, though they present greater control challenges. Here we present ExDex, a dexterous arm-hand system that leverages reinforcement learning to enable non-prehensile manipulation for grasping ungraspable objects. Our system learns two strategic manipulation sequences: relocating objects from table centers to edges for direct grasping, or to walls where extrinsic dexterity enables grasping through environmental interaction. We validate our approach through extensive experiments with dozens of diverse household objects, demonstrating both superior performance and generalization capabilities with novel objects. Furthermore, we successfully transfer the learned policies from simulation to a real-world robot system without additional training, further demonstrating its applicability in real-world scenarios. Project website: https://tangty11.github.io/ExDex/.
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