  We report two surprising results regarding the nature of the spatial broken
symmetries in the two-dimensional (2D), quarter-filled band with strong
electron-electron interactions. First, in direct contradiction to the
predictions of one-electron theory, we find a coexisting ``bond-order and
charge density wave'' (BCDW) insulating ground state in the 2D rectangular
lattice for all anisotropies, including the isotropic limit. Second, we find
that the BCDW further coexists with a spin-density wave (SDW) in the range of
large anisotropy. Further, in contrast to the interacting half-filled band, in
the interacting quarter-filled band there are two transitions: first, a similar
singlet-to-AFM/SDW transition for large anisotropy and second, an
AFM/SDW-to-singlet transition at smaller anisotropy. We discuss how these
theoretical results apply to the insulating states that are proximate to the
superconducting states of 2:1 cationic charge-transfer solids (CTS).
  An important consequence of this work is the suggestion that organic
superconductivity is related to the proximate Coulomb-induced BCDW, with the
SDW that coexists for large anisotropies being also a consequence of the BCDW,
rather than the driver of superconductivity.
