An isolated fragment of basketry is more or less flat. Three-dimensional forms, typically containers, are usually made by changing the number of strands at places in the periodic pattern in order to introduce corners. Three- dimensional baskets without corners, created using hexagonal open weave, are possible within limits determined by internal forces, and models of three of the four elementary topological closed surfaces are described. Such baskets have features in common with both tensegrity structures and Leonardo grids but there are also differences. All three depend on balanced forces, but the ways those forces act are not the same.