  We show that the simultaneous driving of a polariton condensate with both
nonresonant and n^th order resonant pump frequencies allows for a generic
mechanism of breather formation; from this, we construct for the second-order
resonance a family of exotic breathers with nontrivial discrete order of
rotational symmetry. Finally, we demonstrate the spontaneous emergence of both
crystalline and glassy orderings of lattices of polygonal breathers, depending
on the degree of polygonal excitations at the lattice sites.
