  We consider the pairing state due to the usual BCS mechanism in substances of
cubic and hexagonal symmetry where the Fermi surface forms pockets around
several points of high symmetry. We find that the symmetry imposed on the
multiple pocket positions could give rise to a multidimensional nontrivial
superconducting order parameter. The time reversal symmetry in the pairing
state is broken. We suggest several candidate substances where such ordering
may appear, and discuss means by which such a phase may be identified.
