  We present an effective theory for the Bloch functions of a two-dimensional
square lattice near a quadratic degeneracy point. The degeneracy is protected
by the symmetries of the crystal, and breaking these symmetries can either open
a bandgap or split the degeneracy into a pair of linear degeneracies that are
continuable to Dirac points. A degeneracy of this type occurs between the
second and third TM bands of a photonic crystal formed by a square lattice of
dielectric rods. We show that the theory agrees with numerically computed
photonic bandstructures, and discuss the resulting insight into the
reflection-free edge modes induced by parity breaking.
