A variety of structural transitions in nature do not involve a group-subgro
up relationship. A two-dimensional example is the transition between a squa
re lattice and a triangular lattice, which is known to occur in vortex latt
ices, Wigner crystals, skyrmion lattices, colloids, diblock copolymers, etc
. A three-dimensional analog is the shock-induced BCC to HCP transition in
iron. We develop a systematic technique that incorporates site symmetry and
yields displacive transition mechanisms and free energy forms for such str
uctural changes. This procedure is demonstrated for the square to triangle
transition.