  We construct exact non-trivial ground states of spin-2 quantum
antiferromagnets on the hexagonal lattice. Using the optimum ground state
approach we determine the ground state in different subspaces of a general
spin-2 Hamiltonian consistent with some realistic symmetries. These states,
which are not of simple product form, depend on two free parameters and can be
shown to be only weakly degenerate. We find ground states with different types
of magnetic order, i.e. a weak antiferromagnet with finite sublattice
magnetization and a weak ferromagnet with ferrimagnetic order. For the latter
it is argued that a quantum phase transition occurs within the solvable
subspace.
