Given a flat-foldable origami crease pattern (a straight-line drawing of a planar graph on a region of the plane) with a mountain-valley (MV) assignment indicating which creases in bend convexly (mountain) or concavely (valley), we may \emph{flip} a face of to create a new MV assignment which equals except for all creases bordering , where we have . In this paper we explore the configuration space of face flips for a variety of crease patterns that are tilings of the plane, proving examples where results in a MV assignment that is either never, sometimes, or always flat-foldable for various choices of . We also consider the problem of finding, given two foldable MV assignments and of a given crease pattern , a minimal sequence of face flips to turn into . We find polynomial-time algorithms for this in the cases where is either a square grid or the Miura-ori, and show that this problem is NP-hard in the case where is the triangle lattice.