It seems the curvature is positive or negative in relation to the overall body of the material. With positive surface curvature we get bubble or shell shaped ob

It seems the curvature is positive or negative in relation to the overall body of the material. With positive surface curvature we get bubble or shell shaped objects which in bulk amount to a very fine powder. If those shells/balls are fused with each other into a regular lattice - most of the structure can be identical (except the fused parts) but the balls become connected holes in a larger rigidly connected body, which is formed by their union. Im guessing that in normal space negative curvature has to imply surfaces which do not bound a space, but which rather extend through a space - a kind of solid.