Figure 1. Topological transitions of a deformed kagome lattice by uniform soft twisting.

Two types of triangles (red and blue) are connected by free hinges at their corners, forming a deformed kagome lattice with primitive vectors a₁, a₂. The angle θ between the triangles defines the twisting coordinate. The blue curve shows (defined in equation (1)) as a function of θ. The 3 white dots on the θ axis represent three critical angles (, and ) where sides of the triangles form straight lines (yellow stripes on the lattices) and topological polarization R_T (shown as black arrows above the axes) changes.