  Among the states of $^{12}$C, there is an important subset of $K$=0 and
$K$=$I$ planar intrinsic states in which the intrinsic motion of the nucleons
are confined in the planar region defined by the three-alpha cluster or by
their generated toroid. The intrinsic nuclear densities of these states are
toroidal in nature. We study these $^{12}$C toroidal states from the
generator-coordinate viewpoints in both the alpha cluster model and the
toroidal shell model. Numerical solutions in the toroidal mean field
approximation are examined to pave the way for future extensions and
refinements.
