Auxetic networks with no re-entrant polygons

It is widely assumed that auxetic (i.e. negative Poissonu0027s ratio) structures must contain re-entrant polygons in $2$D and re-entrant polyhedra in $3$D. Here we show how to design $2$D auxetic networks with only convex polygons. The design principles used allow for any Poisson ratio $-1 simeq 6$ and $nu simeq 0.33$ and removing those edges that decrease the shear modulus by the least without creating any re-entrant polygons, the system evolves monotonically towards the isostatic point with $ simeq 4$ and $nu simeq -1$.