Fig. 1. (a) Square and (b) kagome lattices with NN springs of spring constant k and NNN springs of spring constant k’. White circles in (a) and white triangles in (b) show a zero-energy distortion. (c) A sequence of twisted kagome lattices. Pulling the purple lattice along the horizontal axis cause it to expand in both the horizontal and vertical directions to the pink and grey lattices, the defining characteristic of auxetic materials. Twisted kagome lattices with triangles at angle a to horizontal.