Regular network of contacting cylinders with implications for materials with negative Poisson ratios

A nontrivial periodic network of contacting infinite rigid cylinders is given. It is shown that the mutual contact constraints can exhaust all the degrees of freedom of the network but one, which is the primary cell size. In effect, the network can only expand or shrink uniformly, exhibiting the extreme Poisson ratio of -1. This may explain why inorganic and biological fibrous materials often have negative Poisson ratios and shows a way to design tubular or fibrous structural units for auxetic materials.