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We identify a class of novel low energy phases of the hydrogen storage material LiAlH4 by using the ab initio minima hopping crystal structure prediction method. These phases are, unlike previous predictions and known structures of similar materials, characterized by polymeric networks consisting of Al atoms interlinked with H atoms. The most stable structure is a layered ionic crystal with P21/c symmetry, and it has lower free energy than the previously reported structure over a wide range of temperatures. Furthermore, we carry out x-ray diffraction, phonon, and GW band-structure analysis in order to characterize this phase. Its experimental synthesis would have profound implications for the study of dehydrogenation and rehydrogenation processes and the stability problem of LiAlH4 for hydrogen storage applications.