  Low-energy structures of alanates are currently known to be described by
patterns of isolated, nearly ideal tetrahedral [AlH$_4$] anions and metal
cations. We discover that the novel polymeric motif recently proposed for
LiAlH$_4$ plays a dominant role in a series of alanates, including LiAlH$_4$,
NaAlH$_4$, KAlH$_4$, Mg(AlH$_4$)$_2$, Ca(AlH$_4$)$_2$ and Sr(AlH$_4$)$_2$. In
particular, most of the low-energy structures discovered for the whole series
are characterized by networks of corner-sharing [AlH$_6$] octahedra, forming
wires and/or planes throughout the materials. Finally, for Mg(AlH$_4$)$_2$ and
Sr(AlH$_4$)$_2$, we identify two polymeric phases to be lowest in energy at low
temperatures.
