These structures are about deformation, flexibility, and form and explore the relationship between innate material properties and bulk mechanical properties through intentional structuring of the material. This deliberate design of the material gives it unique properties, two of which are especially interesting: synclastic bending and auxetic behavior. Synclastic materials have the fascinating ability to assume compound curvature along two (often orthogonal) directions
(see here for a basic illustration of synclastic bending). One can wrap a sphere easily in a synclastic material without folding it whereas attempting the same with an anticlastic material, such as paper, would require numerous folds. Auxetic behavior is found in materials with a negative Poission's ratio, which relates the deformation in one direction when the material is stressed in a perpendicular direction (See here for an illustration). When compressed in one direction, auxetic materials contract in the other, and when stretched, they expand. In other words, an auxetic nail would become narrowed as it was hammered into a board and expand in diameter when pulled out of the board. In addition to their compelling mechanical properties, these mesostructured materials diffuse light nicely and pleasantly pattern-rich. I am exploring applications of the material as both a composite core and for use in light fixtures and furniture.
More background on these structures can be found on my blog.
These print well on the Makerbot Replicator 2 using "Standard" and "Low" slice settings. Backlash can be a problem for the finer structures. Note also that unless your slicer has case handling for thin walls, you will not be able to print some of these geometries. Makerware does handle thin walls, so Makerbot users should be fine.