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Graph neural networks (GNNs) have been shown promising in improving the efficiency of learning communication policies by leveraging their permutation properties. Nonetheless, existing works design GNNs only for specific wireless policies, lacking a systematical approach for modeling graph and selecting structure. Based on the observation that the mismatched permutation property from the policies and the information loss during the update of hidden representations have large impact on the learning performance and efficiency, in this paper we propose a unified framework to learn permutable wireless policies with multidimensional GNNs. To avoid the information loss, the GNNs update the hidden representations of hyper-edges. To exploit all possible permutations of a policy, we provide a method to identify vertices in a graph. We also investigate the permutability of wireless channels that affects the sample efficiency, and show how to trade off the training, inference, and designing complexities of GNNs. We take precoding in different systems as examples to demonstrate how to apply the framework. Simulation results show that the proposed GNNs can achieve close performance to numerical algorithms, and require much fewer training samples and trainable parameters to achieve the same learning performance as the commonly used convolutional neural networks.