What do fabrics with 1000s of interwoven yarns, kitchen strainers with 100s of plastically deforming wires, and architectural gridshells or medical stents with 10s of elastically deforming rods all have in common?

Their geometry: a shell-like grid of flexible but inextensible rods. In 1878, Russian mathematician P. Chebyshev showed how to encode the inextensibility of two families of flexible rods in the language of differential geometry.

In this talk, we see that Chebyshev net geometries apply across vastly different length scales and material properties. I will discuss a series of collaborative efforts in computational fabrication and inverse design. Theoretical obstructions expose the challenges in finding Chebyshev nets on surfaces with large amounts of curvature, suggesting a limited shape space. However, we show that a careful reformulation of the problem, combined with a discrete analog of Chebyshev nets, leads to computational tools that reveal a vibrant design space.