Regularly configured structures with polygonal prisms for three-dimensional auxetic behaviour.

We report here structures, constructed with regular polygonal prisms, that exhibit negative Poisson's ratios. In particular, we show how we can construct such a structure with regular -gonal prism-shaped unit cells that are again built with regular -gonal component prisms. First, we show that the only three possible values for are 3, 4 and 6 and then discuss how we construct the unit cell again with regular -gonal component prisms. Then, we derive Poisson's ratio formula for each of the three structures and show, by analysis and numerical verification, that the structures possess negative Poisson's ratio under certain geometric conditions.