Reconfigurable, expandable-collapsible structures based upon negative Poisson's ratio (NPR) auxetic unit cells achieve rapidly deployable apparatus, devices and systems. A plurality of joint bodies, each joint body having a plurality of connection features, are coupled to interconnecting link members with opposing ends, each end including connection features that engage with the connection features of the joint bodies. The link members pivot about different axes relative to the joint bodies, thereby forming an expandable and collapsible structure having a height and a width. The link members form an array of geometric unit cells when the structure is expanded, and the height and the width of the structure when expanded are both greater than the height and the width of the structure when collapsed. In certain embodiments the structures have unit cells based upon triangles or bowtie shapes.