I'll talk about various theoretical and (via 3D printed models) practical designs for two- and three-dimensional auxetic mechanisms, each with a single degree of freedom. Auxetic mechanisms expand in all directions when pulled on. The classic example is the Hoberman sphere, a network of hinged arms formed into a sphere whose radius increases as the mechanism flexes. I'll talk about examples which are truly three-dimensional auxetics, tiling three-dimensional space rather than a two-dimensional surface. I'll also talk about recent work based on rack and pinion gearings in place of linkages.