  Dirac's quantization of the (2+1)-dimensional analog of Ashtekar's approach
to quantum gravity is investigated. After providing a diffeomorphism-invariant
regularization of the Hamiltonian constraint, we find a set of solutions to
this Hamiltonian constraint which is a generalization of the solution
discovered by Jacobson and Smolin. These solutions are given by particular
linear combinations of the spin network states. While the classical
counterparts of these solutions have degenerate metric, due to a \lq quantum
effect' the area operator has nonvanishing action on these states. We also
discuss how to extend our results to (3+1)-dimensions.
